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Quiver A quiver is a container for arrows, crossbow bolts or darts[?], such as those fired from a bow, crossbow or blowpipe[?]. A quiver may have different forms depending on where it is supposed to be used: Quivers could hang from an archer's belt, from the saddle[?] of a horse or be worn on the back (as most often done in Robin Hood films). If K is a field and Γ is a quiver, then the quiver algebra KΓ is defined as follows: it is the vector space having all the paths in the quiver as basis; multiplication is given by composition of paths. www.ebroadcast.com.au /lookup/encyclopedia/qu/Quiver.html   (315 words)

Quiver (mathematics) - Wikipedia, the free encyclopedia They are commonly used in representation theory: a representation, V, of a quiver assigns a vector space V(x) to each vertex x of the quiver and a linear map V(a) to each arrow a. If K is a field and Γ is a quiver, then the quiver algebra or path algebra KΓ is defined as follows: it is the vector space having all the paths in the quiver as basis; multiplication is given by composition of paths. If the quiver has finitely many vertices and arrows and the end vertex and starting vertex of any path are always distinct, then KΓ is a finite-dimensional hereditary algebra over K, i.e. en.wikipedia.org /wiki/Quiver_(mathematics)   (436 words)

Geometry of quiver-representations The study of representations of quivers encompasses many problems in linear algebra, for example Kronecker's classification of matrix pencils [Kre], and the problem of classifying quadruples of subspaces in a vector space, solved by Gelfand and Ponomarev [GP]. To study the 'geometry of quiver-representations' means to study the algebraic variety which classifies the representations of a quiver of a fixed dimension vector, as well as related varieties, including moduli spaces in the sense of geometric invariant theory. The behaviour of the representations of a quiver turns out to be controlled by the Lie algebra whose graph is obtained from the quiver by forgetting the directions of the arrows. www.amsta.leeds.ac.uk /~pmtwc/quiver   (767 words)

Quiver Mutation in Java   (Site not responding. Last check: 2007-10-08) Quiver mutation is related to a large number of subjects in mathematics and to Seiberg duality in physics, cf. A quiver is an oriented graph: it has vertices (nodes) and arrows between the vertices. It cannot be transformed to a quiver containing arrows of multiplicity 3 or greater. www.math.jussieu.fr /~keller/quivermutation   (444 words)

Your Sail Quiver: Playing the percentages Having a balanced quiver is vital to maximizing your time on the water versus your local conditions. Notice that the gap between a 3.0 and a 4.0 is 33%, but the gap between a 6.0 and a 7.0 is 17%. When you start using a more balanced quiver it becomes apparent that it is more important to have your gap sizes evenly spaced out than the actual sail sizes. www.iwavesolutions.com /lefebvre/Windsurfing/Articles/quiver.html   (523 words)

Interaction of Finite Dimensional Algebras with other areas of Mathematics Methods concerning quivers and their representations have been used in the past 30 years extensively in order to describe the structure of length categories (abelian categories where every object has a finite composition series) which arise very frequently not only in algebra, but also in geometry and analysis. These algebras may be viewed as generalizations of quiver algebras more appropriate for understanding the standard module/irreducible module relationship in the category$\Cal O$, perverse sheaves, and categories of representations of algebraic groups in positive characteristic. Tilting modules, an older development originating in quiver theory, now impact many areas of representation theory, especially characteristic p, through work of Ringel, Donkin, Soergel and Andersen, for example, and have even proved useful for the study of maximal subgroups of finite groups of Lie type (Seitz, Saxl). www.pims.math.ca /birs/workshops/2004/04w5501   (1176 words)

Clay Mathematics Institute A quiver is an oriented graph; a representation of a quiver is an assignment of a vector space to each vertex and of a linear map to each oriented edge of the quiver. On the contrary, for a general quiver, the classification of finite dimensional representations is known to be a wild problem, that is, no such classification could possibly exist. Quivers in Algebra, Geometry, and Representation Theory (Victor Ginzburg) www.claymath.org /programs/outreach/academy/colloquium2005.php   (1046 words)

Graph (mathematics) Summary Graphs are used extensively throughout the fields of mathematics, statistics, science, engineering, business, and research in order to depict information--whether a mathematical curve of statistical data--in a form that humans find easy to process. In mathematics and computer science, a graph is the basic object of study in graph theory. A quiver is sometimes said to be simply a directed graph, but in practice it is a directed graph with vector spaces attached to the vertices and linear transformations attached to the arcs. www.bookrags.com /Graph_(mathematics)   (3202 words)

Jerusalem Mathematics Colloquium   (Site not responding. Last check: 2007-10-08) The Jerusalem Mathematics Colloquium is happy to host the first of three lectures given as part of the annual Zabrodsky lecture series. Abstract: This lecture is designed to be understood by a general mathematical audience, including graduate students with some background in basic algebraic concepts (such as would be covered in an introductory graduate course in algebra, plus low-level familiarity with the concept of an affine/projective algebraic variety). In particular, this will lead us to representations of algebras given by quiver and relations, which are located at the heart of this sequence of talks (we will introduce them here, no prior familiarity is required). www.ma.huji.ac.il /~colloq/2005-06/col.051124.html   (509 words)

Springer Online Reference Works   (Site not responding. Last check: 2007-10-08) some field, for example the path-algebra of some finite quiver without oriented cycles. Moreover, the Auslander–Reiten quiver of a tilted algebra always contains pre-projective and pre-injective components.  C.M. Ringel,   "The regular components of the Auslander–Reiten Quiver of a tilted algebra"  Chinese Ann. eom.springer.de /t/t130100.htm   (443 words)

Amazon.com: Quiver: Books: Stephanie Spinner   (Site not responding. Last check: 2007-10-08) I suppose that injustice is part of what makes "Quiver" so convincing and evocative of the original myths it is based on. Quiver was a wonderful integration of mythology, romance, and adventure. Spinner's Quiver was a delicate mix of the many tales of Atalanta. www.amazon.com /Quiver-Stephanie-Spinner/dp/0375814892   (1784 words)

Quiver diagram - Wikipedia, the free encyclopedia In physics, a quiver diagram is a graph representing the matter content of a gauge theory that describes D-branes on orbifolds. The relevance of quiver diagrams for string theory was pointed out and studied by Michael Douglas and Greg Moore. While string theorists use the words quiver diagram, many of their colleagues in particle physics call these diagrams mooses. en.wikipedia.org /wiki/Quiver_diagram   (121 words)

UM Mathematics If we attach to each vertex a vector space and to each arrow a linear map, then this is called a representation of the quiver Q. Quiver representations give a natural generalization of some linear algebra problems. There are several reasons for studying quiver representations. I am particularly interested in the connection between quiver representations and the representation theory of GLn. www.math.lsa.umich.edu /people/facultyDetail.php?uniqname=hderksen   (528 words)

AFRICAN DIASPORA JOURNAL OF MATHEMATICS In this paper, a mathematical model is proposed to study the depletion of forest biomass by different levels of industrialization in two different adjoining regions of the habitat leading to patchiness. In the model it is assumed that the density of forestry resource biomass is governed by the same logistic equation with the prescribed intrinsic growth rate and carrying capacity in both the regions. The mathematical properties of the resulting distributions are studied. www.african-j-math.org /eprints.htm   (4640 words)

NISC South Africa Noetherian quivers have been studied and characterized (when the number of arrows is finite) by Höinghuas and Richter in [10]. In this paper we give a characterization of noetherian quivers in the most general case in Theorem 3.6. We prove that a quiver is noetherian if and only if the rooted tree associated to any vertex satisfies some sort of finiteness condition, if and only if every finitely generated representation over a noetherian ring has an injective cover. www.nisc.co.za /oneAbstract?absId=607   (162 words)

Curriculum Vitae of Harm Derksen Coorganizer of the worshop Geometry of Quiver Representations, Oberwolfach, Germany, April 2003. The kernel of a derivation/Inverse degrees and the Jacobian Conjecture, Krakow, Poland. Harm Derksen, Jerzy Weyman, Semi-invariants of quivers and saturation for Littlewood-Richardson coefficients, J. Amer. www.math.lsa.umich.edu /~hderksen/CV/CV.html   (1268 words)

Dialogos of Eide: LIGO Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition. Well I created another triangle, but it is a little different model, and does not use numbers for mathematic discretion as a emergent property of first principal. A great mathematical theory should similarly be beautiful on both large and small scales. eskesthai.blogspot.com /search/label/LIGO   (10585 words)

ARCC Workshop: Arithmetic harmonic analysis on character and quiver varieties Via the Riemann-Hilbert monodromy map they are related to the character variety which is the representation variety of the fundamental group of the Riemann surface to a complex reductive Lie group. Recently it was found that arithmetic methods could be used to study their cohomology, and in turn relate them to the representation theory of finite groups of Lie type. The analogue arithmetic study on quiver varieties leads to the representation theory of finite Lie algebras. www.aimath.org /ARCC/workshops/charvarieties.html   (560 words)

Curriculum Vitae of Alexander Yong   (Site not responding. Last check: 2007-10-08) University of Michigan at Ann Arbor, Ph.D. in Mathematics (2003). IAS/Park City Mathematics Institute (PCMI), Park City, Utah, July 2004. Address: Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720-3840, USA. math.berkeley.edu /~ayong/cv.html   (915 words)

Research of Michael Barot Definition of quiver, representation of a quiver and a morphism between two representations. The problem is explained and studied in three examples: the linear quiver, the loop and the three Kronecker. A concrete recipe to construct all derived tubular algebras which are reflection equivalent to given tubular algebra is given. www.matem.unam.mx /barot/research.html   (1019 words)

quiver - OneLook Dictionary Search Phrases that include quiver: full quiver, quiver diagram, sutherland brothers and quiver Words similar to quiver: chill, flicker, flitter, flutter, frisson, palpitation, quake, quivered, quivering, quiveringly, shakiness, shaking, shiver, shudder, thrill, tingle, trembling, tremor, vibration, waver, more... This is a OneLook Word of the Day, which means it might be in the news. www.onelook.com /?w=quiver&loc=wotd   (287 words)

QUIVER GAUGE THEORIES Can someone define the term quiver gauge theory for me\nandgt; or refer me to an earlier hep-th paper where the term is defined?\nandgt; Thanks! A quiver is a directed graph, ie, dots with arrows between them. georgie\nandgt;\nandgt; A quiver is a directed graph, ie, dots with arrows between them. www.physicsforums.com /showthread.php?t=82813   (568 words)

[No title]   (Site not responding. Last check: 2007-10-08) Buch and Fulton defined quiver polynomials in a geometric context, and proved that these polynomials can be expressed as integer sums of products of Schur functions in differences of alphabets. Motivated by the fact that Littlewood-Richardson numbers are (very) special cases of the integer `quiver coefficients' appearing in these sums, Buch and Fulton conjectured that all quiver coefficients are positive, and moreover described certain `factor sequenes' of Young tableaux that they should count. The first thing I'll do in this talk is present an elementary definition of quiver polynomials, with no reference to geometry, in terms of combinatorial permutation diagrams called `pipe dreams' (`rc-graphs'). www-math.mit.edu /~combin/abstracts/mar03/miller.html   (160 words)

ARCC: American Institute of Mathematics Research Conference Center The AIM Research Conference Center (ARCC) hosts focused workshops in all areas of the mathematical sciences. ARCC focused workshops are distinguished by their emphasis on a specific mathematical goal, such as making progress on a significant unsolved problem, understanding the proof of an important new result, or examining the convergence of two distinct areas of mathematics. The leaders in each field are involved in the planning of the workshops, and junior scientists and graduate students are active participants. www.aimath.org /ARCC   (284 words)

week230 There are cool relationships between quivers and quantum groups, which tie this item to the rest. These extended graphs are the result of adding one (particular) vertex to each of the ADE graphs, and they often arise as the answer to questions that are just slightly weaker than the questions answered by the ADE graphs. This gives a high motivation to look for new concepts and it shows that simple and since long understood mathematics can still raise very interesting questions, show paths for new research and give a glance at the mystery of mathematics. math.ucr.edu /home/baez/week230.html   (4835 words)

[No title] [4] Moduli of McKay quiver representations I: the coherent component, (with Alastair Craw and Diane Maclagan), to appear in Proceedings of the London Math. [5] Moduli of McKay quiver representations II: Groebner basis techniques, (with Al\astair Craw and Diane Maclagan), to appear in Journal of Algebra, math.AG/0611840. [11] The associated primes of initial ideals of lattice ideals, (with Serkan Hosten), Mathematical Research Letters 6 (1999) 83-97. www.math.washington.edu /~thomas/papers/articles.html   (671 words)

Lieven Le Bruyn's Storefront - Lulu.com The second volume will focuss on applications to moduli spaces, quiver varieties and singularities. noncommutative geometry@n – the trade contains applications to the material developed in volume 1 - the tools to moduli spaces, quiver varieties and singularities. It details the representation theory of Cayley-smooth and Quillen-smooth algebras by studying the geometry of the quotient varieties and relating the Hesselink stratification of their nullcones to moduli spaces of quiver-representations. www.lulu.com /neverendingbooks   (250 words)

Einstein Institute of Mathematics, The Hebrew University - Zabrodsky Memorial Symposium Einstein Institute of Mathematics, The Hebrew University - Zabrodsky Memorial Symposium The Institute of Mathematics invites you to this year's Annual Lecture Series in Topology and Geometry in memory of Prof. ABSTRACT: The only additional prerequisite required for this talk is the material of the overview lecture. www.ma.huji.ac.il /conf/zabrodsky.html   (624 words)

Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform -- Hausel 103 (16): 6120 -- ... Mathematical Institute, University of Oxford, Oxford OX1 3LB, United Kingdom; and Department of Mathematics, University of Texas, Austin, TX 78712 and Poincaré polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number www.pnas.org /cgi/content/abstract/103/16/6120   (219 words)

KITP Program: Mathematical Structures in String Theory in partnership with the Clay Mathematics Institute, and coordinated by New Sasaki Einstein Metrics and Their Dual Quivers Mathematical Foundations for the Study of Poincare-Einstein Spaces online.kitp.ucsb.edu /online/strings05   (325 words)

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