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[No title] Algebraic structures of the classical mechanics is a limited case of the algebraic structures (2.3), (2.4): the pointwise product and the Poisson bracket may be derived from the Jordan-Moyal product and the Poisson-Moyal bracket by passing to the limit $% \hbar \to 0$. The algebraic structures of standard operator quantum mechanics and the WWM representation are connected by the Weyl-Wigner correspondence rule \begin{equation} -{\frac{i}{\hbar}} [\hat f, \hat g ] \to {\{f,g\}}_M ; \qquad {\frac{1}{2}} {% [\hat f, \hat g ]}_+ \to f \circ g. Hence, for a construction of nonclassical algebraic structures it is necessary to use an infinite linear combination of all $\{\cdot,\cdot\}^{(k)},\quad k\geq0$. www.ma.utexas.edu /mp_arc/papers/97-563   (2507 words)

Allan Donsig's research page   (Site not responding. Last check: 2007-10-21) This invariant is complete for a certain family of limit algebras: inductive limits of digraph algebras (a.k.a.\ finite dimensional CSL algebras) satisfying two conditions: (1) the inclusions of the digraph algebras respect the order-preserving normalisers, and (2) the digraph algebras have chordal digraphs. If the algebra is also a CSL algebra, we scharacterize when the first homology group of the algebra is contained in the first homology group of the (4,4) entry; in these cases, the only obstruction to a derivation being inner arises from the (4,4) entry. In the present paper, we weamine the clase of nest algebras T in AF -algebras which share the distinctive properties of the refinement algebra: (1) T is a nest algebra in which the nest generated the diagonal, (2) T admits a locally constant cocycle. www.math.unl.edu /~adonsig/research.html   (2559 words)

Invariant Discretization Methods for n-Dimensional Nonlinear Reactive Transport Models   (Site not responding. Last check: 2007-10-21) Invariant re-mapping transformations reconstruct tangled Lagrangian grids, re-map the conserved and non-conserved constitutive physical cell parameters from arbitrary Eulerian to Lagrangian discretizations, and conservatively re-map advected constitutive physical cell parameters on Eulerian grids, while preserving the invariant geometric-algebraic symmetry of the grids that numerically discretize the physical domain space and solve the system of PDEs. These representations are order theoretic generalizations of the convex face geometry of any grid complex, and carry the invariant geometric properties of the grid that numerical discretization depends on (e.g., edge lengths, areas of faces, volumes of cells, and angles between edges, etc.). We are constructing a new class of combinatorial methods, based on symmetry-invariant re-mapping and coordinate-free incidence algebra representations of the geometric face lattices of grid complexes, which preserve the invariant physical symmetries of the physical problem domain. www.emsl.pnl.gov /docs/tms/annual_report1999/1619b-2c.html   (1210 words)

The Algebra of an Invariant Ring and Algebraic Relations This function also returns a sequence Q giving the secondary invariants in terms of the irreducible secondary invariants as monomials in A. Thus Q[i] is the monomial p_i(t_i) mentioned in the introduction to this section. Given an invariant ring R=K[V]^G, return the ideal of algebraic relations corresponding to R. This is simply the same as taking the ideal generated by the algebra A by the sequence L returned by the function Relations(R). Given an invariant ring R=K[V]^G, return the algebra corresponding to the primary invariants of R as a graded polynomial ring (with the weights corresponding to the degrees of the primary invariants). www.math.wisc.edu /help/magma/text424.html   (569 words)

MATH 7512: Topology II The basic idea of this subject is to associate to a topological space an algebraic object (a polynomial, a group, a ring, etc.) in such a way that topologically equivalent spaces get assigned equivalent objects (e.g., the same polynomial, isomorphic groups). Such an algebraic object is an invariant of the space, and provides a means for distinguishing between topological spaces: if two spaces have inequivalent invariants, they cannot be topologically equivalent. The focus of MATH 7512 is on one such algebraic invariant, the fundamental group (consisting, loosely speaking, of unshrinkable loops in the topological space in question). www.math.lsu.edu /~cohen/courses/PastSemesters/SPRING00/T1F98.html   (564 words)

Algebraic Geometry Algebraic Geometry is a new emphasis area within the department. Algebraic Geometry in simplest terms is the study of polynomial equations and the geometry of their solutions. The document Graduate Studies in Algebraic Geometry outlines the general areas of Algebraic Geometry studied here and describes the advanced undergraduate and graduate courses that are under development or offered regularly. www.math.uiuc.edu /ResearchAreas/AlgebraicGeometry   (324 words)

Invariant of a Pair of Non-coplanar Conics in Space: Definition, Geometric interpretation and Computation - Quan ... In this paper, the algebraic invariant of a pair of non-coplanar conics in space is concerned. The algebraic invariant of a pair of non-coplanar conics is first derived from the invariant algebra of a pair of quaternary quadratic forms by using the dual representation of space conics. Then, this algebraic invariant is geometrically interpreted in terms of cross-ratios. citeseer.ist.psu.edu /18768.html   (868 words)

QTDS url > II Symposium on Planar Vector Fields We apply the Darboux theory to study the integrability of real quadratic differential systems having an invariant conic.The fact that two intersecting straight lines or two parallel straight lines are particular cases of conics allows us to study simultaneously the integrability of quadratic systems having at least two invariant straight lines real or complex. Darboux in 1878 was the first in showing the fascinating relationships between the integrability (a topological phenomena) and the existence of invariant algebraic curves. That is, $\Gamma$ is an invariant analytic curve for which there is a neighbourhood composed of integral curves $\gamma$ of $X$ that {\em spiral\/} asymptotically around the axis $\Gamma$ and have flat contact with it. web.udl.es /usuaris/y4370980/sympo2.html   (3425 words)

[No title] Frank Grosshans: The invariants of unipotent radicals of parabolic subgroups. How to compute a set of generators for the ring of invariant functions in the case where the characteristic of the ground field is prime. Conjeeveram Seshadri: On a theorem of Weitzenboeck in invariant theory. felix.unife.it /Root/d-Mathematics/d-Algebraic-geometry/b-Algebraic-groups-and-invariant-theory   (365 words)

Pure Mathematics Research, Department of Mathematics, Univ. of Manchester, UK In invariant theory of algebraic groups, we work on generalising well-known results of Andreev, Vinberg, Elashvili and A.M. Popov on complex linear G-actions with nontrivial generic stabilisers to the case where G is a semisimple group over a field of positive characteristic. It is established that a similar relationship exists between the algebras arising in subregular representation theory and noncommutative deformations of Klein singularities similar to those introduced recently by Hodges, Crawley-Boevey and Holland. Modular representation theory of Lie algebras is now a very active and attractive field due to deep interactions with representation theory of quantum groups at roots of unity and some recent discoveries such as Premet's proof of the Kac-Weisfeiler conjecture and Jantzen's work on subregular nilpotent representations. www.ma.man.ac.uk /DeptWeb/Groups/Pure/Algebra.html   (498 words)

Invariant theory - Wikipedia, the free encyclopedia A recent resource for learning about modular invariants of finite groups. An undergraduate level introduction to the classical theory of invariants of binary forms (but not the Omega process!). A beautiful introduction to the theory of invariants of finite groups and techniques for computing them using Gröbner bases. en.wikipedia.org /wiki/Invariant_theory   (495 words)

[No title] The command is thought to avoid time consuming algebraic conversions by generating immediately the numerical values of the vertices of the polygons to be drawn. The Bryant data of this curve are g[z] and the difference of the squares of the Schwarzian derivatives of f and g divided by 4 g'[z]. The commutator X=[X1,X2] of these is a new left invariant vector field on Sl(2,C), defined in the sense of the basic notion the commutator of two vector fileds in differential geometry. www.mathematik.hu-berlin.de /~gollek/CMC/cmc1.m   (5214 words)

Citations: Robust algebraic invariant methods with applications in geometry and imaging - Barrett, Payton, Gheen ...   (Site not responding. Last check: 2007-10-21) In other words, given two model views and a tensor, the third view is uniquely determined and can be synthesized by means of a warping function applied to the two model images. Robust algebraic invariant methods with applications in geometry and imaging. Namely, if N 3 views are given what is the best way to represent the algebraic relations among them One possibility is to seek higher order tensors beyond four views.... citeseer.lcs.mit.edu /context/14810/0   (1157 words)

Junior Geometry: abstracts This invariant is sometimes—I expect always—equal to the Seiberg–Witten invariant of the underlying four-manifold. Operads are a formalization of the notion of algebraic structure. Hirzebruch's generalisation is harder to understand: he expresses the holomorphic Euler characteristic of a vector bundle E on a complex manifold M as a polynomial in the Chern classes of E and of M. The aim of this talk is to bridge the gap by looking at the case of complex surfaces. www.ma.ic.ac.uk /juniorgeometry/abstracts.html   (6353 words)

[No title] For an algebraic group G, defined over an algebraically closed field of characteristic zero, there is a natural partial order on the set of G-actions on algebraic varieties: X >= Y if there exists a dominant G-equivariant rational map (i.e., a compression) from X to Y. Alternatively, one can consider regular, rather than rational, compressions. The essential dimension is a numerical invariant of the group; it is often equal to the minimal number of independent parameters required to describe all algebraic objects of a certain type. In this paper we classify the smooth closed subvarieties of Alg_r which are invariant under the transport of structure action and study the singularities which may occur. www.math.ubc.ca /~reichst/abstract.html   (2805 words)

Amazon.ca: Books: Algebraic L-Theory and Topological Manifolds   (Site not responding. Last check: 2007-10-21) For those readers who have completed advanced studies in algebraic topology and K-theory, and are ready to move on to a few of the even more esoteric topics in algebra and topology, this book would be an excellent choice. The algebraic L-theory assembly map essentially measures how far a homotopy equivalence is from being homotopic to a homeomorphism, or, put another way, how far from being rigid a space is (a rigid manifold is one in which every homotopy equivalence is homotopic to a homeomorphism). This algebraic theory is then related to the geometric/topological context in the second half of the book. www.amazon.ca /exec/obidos/ASIN/0521420245   (1187 words)

ALGEBRA SEMINAR Then, I shall apply it to sketch a candidate for a {\it noncommutative algebraic geometry}. The final part of the talk is devoted to invariant and moduli theory, and to some non-trivial examples where the algebraic structure of the set of orbits for a group-action on a k-variety turn out to be non-commutative. In particular I shall treat the case of iso-classes of endomorphisms in dimension 2 and 3. www.math.ku.dk /cal/events/1209.htm   (97 words)

FIM - Introduction to Algebraic Transformation Groups and Invariant Theory Invariant theory has a history that is almost one-and-a-half centuries long. Invariants came into existence as a tool to distinguish (and, ultimately, to classify) non-equivalent objects in algebraic problems where the equivalence relation is usually given by the action of a group on a set. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection has not been achieved until recently when invariant theory was in fact subsumed by a general theory of algebraic transformation groups. stat.ethz.ch /fim/activities/eth_lectures/archive/ws0203/popov/?   (341 words)

Search Results for Groups Her thesis was on The algebraic groups of spherical trigonometry and Klein discusses the results in one of his books. Starting with an analysis of the geometrical configuration formed by the centres and the invariant primes of the homologies, she was able, by a very thorough and careful investigation, to obtain, for each of the groups, the distribution of the operations in conjugate sets, and to make the nature of these operations clear. Third, he handled algebraic equations, sometimes proceeding to the evaluation of roots, and sometimes treating the so-called equation without affect, that is, with symmetric Galois groups. www-groups.dcs.st-and.ac.uk /history/Search/historysearch.cgi?SUGGESTION=Groups&CONTEXT=1   (16506 words)

D. White   (Site not responding. Last check: 2007-10-21) Abstract: Motivic cohomology is an algebraically defined invariant for algebraic varieties that tries to mimic singular cohomology, which is a topologically defined invariant for topological spaces. Abstract: The theory of algebraic groups is an interesting branch of algebraic geometry that has important applications in number theory, invariant theory, and group theory. Each reincarnation has benefited from and contributed to commutative algebra and algebraic geometry, and thus this topic and its history should be of significant interest to us today. www.math.uiuc.edu /~dwhite/gssfall2003.html   (1142 words)

IngentaConnect Algebraic invariant curves of plane polynomial differential syste...   (Site not responding. Last check: 2007-10-21) IngentaConnect Algebraic invariant curves of plane polynomial differential syste... With each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential [iopmath latex="$\omega=~\rmd x/P=~\rmd y/Q$"] =  dx/P =  dy/Q [/iopmath]. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. api.ingentaconnect.com /content/iop/jphysa/2001/00000034/00000003/art00325   (161 words)

Abstracts for Submitted and Published Papers McCallum's projection operator for Cylindrical Algebraic Decomposition (CAD) represented a huge step forward for the practical utility of the CAD algorithm. Quantifier elimination by cylindrical algebraic decomposition (CAD) does this via an intermediate representation of the semi-algebraic set as a CAD. This paper presents a method for simplifying the truth-invariant cylindrical algebraic decomposition (CAD) produced by the stack construction phase of the CAD-based quantifier elimination algorithm. www.cs.usna.edu /~wcbrown/research/abstracts/abstracts/abstracts.html   (741 words)

abstracts.html One natural generalization of this invariant is the character of the representation, which is the function sending a group element g to the trace of the operator ß(g). If ß preserves an invariant Hermitian form, then a second natural refinement of the dimension is the signature of the invariant form. The purpose of the talk is to present a conjecture that links representations of the affine algebra at the critical level with D-modules on the affine Grassmannian. math.arizona.edu /~grt/abstracts.html   (1112 words)

Amazon.de: Bücher: Algebraic Geometry, Vol.4 : Linear Algebraic Groups, Invariant Theory   (Site not responding. Last check: 2007-10-21) The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics. Fachbücher > Mathematik > Algebra & Zahlentheorie > Algebraische Geometrie Fachbücher > Mathematik > Algebra & Zahlentheorie > Lineare Algebra www.amazon.de /exec/obidos/ASIN/3540546820   (435 words)

Amazon.de: Bücher: Algebraic Homogeneous Spaces and Invariant Theory   (Site not responding. Last check: 2007-10-21) The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. The exposition assumes a basic knowledge of algebraic groups and then develops each topic systematically with applications to invariant theory. A review of algebraic homogenous spaces and invariant theory, this work includes examination of observable subgroups, the transfer principle, and invariants of maximal unipotent subgroups. www.amazon.de /exec/obidos/ASIN/3540636285/ww2afvportalinpa   (359 words)

The Algebra of an Invariant Ring and Algebraic Relations Suppose also that primary invariants { f_1,..., f_n } for R have been constructed, together with minimal secondary invariants S = { g_1,..., g_m } for R with respect to these primary invariants. Suppose also that the irreducible secondary invariants for R are S = { h_1,..., h_r } so that the g_i are power products of the h_i. Given an invariant ring R=K[V]^G, return the ideal of algebraic relations corresponding to R. This is simply the same as taking the ideal generated by the algebra A by the sequence L returned by the function math.niu.edu /help/math/magmahelp/text950.html   (561 words)

IP1 Sphere Representations and the Colin de Verdiere Number of a Graph   (Site not responding. Last check: 2007-10-21) The invariant, whose definition was linear-algebraic, generated considerable interest. One of the reasons for this interest was that the invariant was the first linear-algebraic graph invariant that related to topological properties of graphs. In particular, he will discuss a surprising connection with a classical theorem of Koebe on representations of planar graphs by touching circles, and a theorem of Cauchy on the rigidity of convex polytopes in 3-space, and use this connection to characterize the cases when mu is close to n, the number of nodes. www.siam.org /meetings/archives/dm96/ip1.htm   (194 words)

Postgraduate Prospectus 2005/2006   (Site not responding. Last check: 2007-10-21) Dr A Baranov: Lie algebras and representation theory; asymptotic phenomena in Lie algebras, finite and algebraic groups, and their representations; direct limits of finite dimensional algebras and groups. Professor J Hunton: Algebraic topology and applications of K-theoretic and homological techniques to symbolic dynamics, mathematical physics and algebraic systems; quasi periodic patterns; algebraic and coalgebraic structures reflecting geometric, topological and group theoretic phenomena. Dr F Neumann: Algebraic topology and homotopy theory, cohomology of finite loop spaces and generalized homogeneous spaces; algebraic invariant theory; applications of homotopy theory to algebraic geometry and arithmetic geometry, étale homotopy and cohomology of stacks. www.le.ac.uk /ua/hd/pgprospectus/research/sci_mathematics.html   (572 words)

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