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Topic: Lie superalgebra

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Lie algebra

Anyonic Lie algebra

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	Lie superalgebra - TheBestLinks.com - Star Lie superalgebra, Boson, Characteristic, Field (mathematics), ... (Site not responding. Last check: 2007-10-13)
		In mathematics, a Lie superalgebra is a kind of generalisation of a Lie algebra.
		Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry.
		Lie superalgebra is a complex Lie superalgebra equipped with an involutive antilinear map from itself to itself which respects the Z
	www.thebestlinks.com /Star_Lie_superalgebra.html (311 words)

	Tanya Khovanova's List of Publications
		Structure of Lie Superalgebras on Eigenfunctions and Jets of the Kernel of the Resolvent near the Diagonal for an n-th-order Differential Operator.
		Lie Superalgebra Structure on Eigenfunctions and Jets of Resolvent's Kernel, near the Diagonal of an n-th Order Ordinary Differential Operator.
		The stabilizer of this point in the coadjoint action inherits the structure of the Lie superalgebra and can be described as the direct sum of the jets of the kernel of the resolvent of, and the eigenfunctions of, the given differential operator.
	www.tanyakhovanova.com /publications/publlist.html (467 words)

	Lie superalgebras graded by P(n) and Q(n) -- Martínez and Zelmanov 100 (14): 8130 -- Proceedings of the National ... (Site not responding. Last check: 2007-10-13)
		Lie superalgebras graded by P(n) and Q(n) -- Martínez and Zelmanov 100 (14): 8130 -- Proceedings of the National Academy of Sciences
		The Lie superalgebra P(n - 1) is the superalgebra of 2n
		The Lie superalgebra L is centrally isogenous with the Tits-Kantor-Koecher
	intl.pnas.org /cgi/content/full/100/14/8130 (1492 words)

	LIST OF PUBLICATIONS OF TCHAVDAR D. PALEV
		T.D. Palev, Irreducible finite-dimensional representations of the Lie superalgebra sl(1,3).
		A.H. Kamupingene, N.A. Ki, T.D. Palev, Finite-dimensional representations of the Lie superalgebra gl(2/2) in a gl(2) $\oplus$ gl(2) basis.
		T.D. Palev and J. Van der Jeugt, Fock representations of the Lie superalgebra q(n+1).
	theo.inrne.bas.bg /~tpalev/pubp.htm (2266 words)

	PlanetMath: superalgebra
		As a vector space, a superalgebra has a decomposition into two homogeneous ideals,
		This is version 3 of superalgebra, born on 2002-06-09, modified 2004-04-29.
		Object id is 3082, canonical name is SuperAlgebra.
	planetmath.org /encyclopedia/SuperAlgebra.html (96 words)

	[No title]
		Irreducible representations of the Lie superalgebra of vector fields and invariant differential operators (with J. Bernstein).
		Irreducible representations of Lie superalgebras of divergence-free vector field and invariant differential operators.
		The said representations for distinguished simple Lie superalgebras of string theories are described together with semi-infinite cohomology and "critical dimensions" of string theories revisited.
	www.math.su.se /~mleites/pub.html (2630 words)

	Leites' (super)questions
		Cohomology of Poisson and Hamiltonian Lie (super)algebras, with emphasis and low-dimensional cohomology and deformations.
		Golod, A deformation of the affine Lie algebra A
		Poletaeva, Superconformal algebras and Lie superalgebras of the Hodge theory, J. Nonlin.
	www.justpasha.org /math/questions/leites.html (1466 words)

	Stukopin (Site not responding. Last check: 2007-10-13)
		The Yangian Y(g) of classical Lie Superalgebra g (or superYangian) is introduced as a specialization of quantization of the bisuperalgebra of currents g[u] with cosuperalgebra structure defined by rational r-matrix.
		The Yangians of simple Lie algebras play the role of the dynamical symmetries in quantum field theories and are used in investigation of integrable models of quantum mechanics and statistical physics.
		The Yangians of Lie superalgebras of A(m,n) type were described in [3] and its representations were described in [4].
	www.imath.kiev.ua /~snmp2003/abstract2003/Stukopin.html (384 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		A Lie (super)algebra can admit more than one grading, for example, the free Lie (super)algebra on $n$ generators admits a {\bf Z}$_2$-grading, but also admits the length of ``words'' as a grading, or a multigrading where the degree of $x_i$ is the $n$-tuple $(0,\dots,1,\dots,0)$ (1 on the $i$-th place).
		If $\lie$ is a liebracket, these commutators are $\lie(i,i)=0$ for all $i>0$ (this follows directly from the (graded) skew-symmetry and the fact that $x(i)$ is even for $i>0$), $\lie(i,0)$ for $i=-n,\dots,-1$ and $\lie(0,i)$ for $i=0,\dots,m$ (this has been explained in one of the previous sections).
		The most convenient way to implement this is by making a Lie (super)algebra generator a rtype of itself, algebra_generator, and assigning a set-element-function and a clear function to it, which take care of all the necessary actions.
	www.math.utah.edu:8080 /ftp/pub/mirrors/ctan.tug.org/tex-archive/web/reduce/rweb/appl/liesuper.web (17015 words)

	AMCA: Central extensions of the elementary unitary Lie superalgebra by Ana Duff (Site not responding. Last check: 2007-10-13)
		AMCA: Central extensions of the elementary unitary Lie superalgebra by Ana Duff
		Central extensions of the elementary unitary Lie superalgebra
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/l/s/13.htm (133 words)

	Ian M. Musson: Papers/Preprints
		It is further shown that the finite dimensional irreducible modules over a (not necessarily classical) finite dimensional complex Lie superalgebra form a complete set if and only if the even part of the Lie superalgebra is reductive and the universal enveloping superalgebra is semiprime.
		Abstract: We construct $Z_{2}$-graded crystal bases for thequantized universal enveloping algebra of the Lie superalgebra osp(1,2r).
		The invariant $k(\cal O)$ is in many cases, equal to the odd dimension of the orbit $G\cdot\cal O$ where $G$ is a Lie supergroup with Lie superalgebra ${\mathfrak g}$.
	www.uwm.edu /~musson/preprints.html (1159 words)

	Results Page (Site not responding. Last check: 2007-10-13)
		In the case of para-Fermi statistics these relations can be associated with the orthogonal Lie algebra B_n=so(2n+1); in the case of para-Bose statistics they are associated with the Lie superalgebra B(0n)=osp(12n).
		In a previous paper, a mathematical definition of ``a generalized quantum statistics associated with a classical Lie algebra G'' was given, and a complete classification was obtained.
		Just as in the Lie algebra case, this definition is closely related to a certain Z-grading of G. We give in this paper a complete classification of all generalized quantum statistics associated with the basic classical Lie superalgebras A(mn), B(mn), C(n) and D(mn).
	eprints.bo.cnr.it /cgi-bin/show.pl?code=314836&arch=5 (160 words)

	Lie superalgebra structures in H-center dot (g;g) -- from Mathematica Information Center
		Abstract Let g=vect(M) be the Lie (super)algebra of vector fields on any connected (super)manifold M; let ldquo-rdquo be the change of parity functor, C i and H i the space of i-chains and i-cohomology.
		The Nijenhuis bracket makes into a Lie superalgebra that can be interpreted as the centralizer of the exterior differential considered as a vector field on the supermanifold associated with the de Rham bundle on M. A similar bracket introduces structures of DG Lie superalgebra in L * and for any Lie superalgebra g.
		We use a Mathematica-based package SuperLie (already proven useful in various problems) to explicitly describe the algebras l * for some simple finite dimensional Lie superalgebras g and their ldquorelativesrdquo - the nontrivial central extensions or derivation algebras of the considered simple ones.
	library.wolfram.com /infocenter/Articles/5895 (142 words)

	Atlas: The graded Lie superalgebra structure on the Hochschild cohomology of truncated polynomial algebras by Thorsten ... (Site not responding. Last check: 2007-10-13)
		Atlas: The graded Lie superalgebra structure on the Hochschild cohomology of truncated polynomial algebras by Thorsten Holm
		The graded Lie superalgebra structure on the Hochschild cohomology of truncated polynomial algebras
		The Hochschild cohomology of an associative algebra carries the structure of a graded Lie superalgebra induced by the Gerstenhaber bracket.
	atlas-conferences.com /c/a/q/i/64.htm (157 words)

	LIST OF PUBLICATIONS OF NEDIALKA ILIEVA STOILOVA
		T.D. Palev, N.I. Stoilova, Finite-dimensional representations of the Lie superalgebra gl(2/2) in a gl(2) + gl(2) basis.
		T.D. Palev, N.I. Stoilova, Finite-dimensional representations of the basic Lie superalgebra A(1/1) in a sl(2) + sl(2) basis.
		N.I. Stoilova and J. Van der Jeugt, Lie superalgebraic framework for generalization of quantum statistics, in: Lie Theory and Its Applications in Physics VI, Proceedings of the Sixth International Workshop, Varna, Bulgaria 15 - 21 August 2005.
	theo.inrne.bas.bg /~stoilova/pubn.htm (975 words)

	some bibliography: Z (Site not responding. Last check: 2007-10-13)
		Every Lie algebra G such that the operators ad g, $g\in G$, are algebraic of bounded degree, is locally finite-dimensional.
		The uniquiness of the decomposition of quadratic Lie algebras
		Criterion for a Lie algebra over Q to be categorical (roughly, this is equivalent to be finite-dimensional over some field and nondecomposbale into direct sum).
	www.justpasha.org /math/bib/z.html (1352 words)

	Representation Theory
		E. Letzter, A bijection of primitive spectra for classical Lie superalgebras of Type I, J. London Math.
		I. Musson, On the center of the enveloping algebra of a classical simple Lie superalgebra, J. Algebra 193 (1997), 75-101.
		M. Scheunert, The theory of Lie superalgebras, Lecture Notes in Mathematics, 716, Springer-Verlag, Berlin, 1979.
	www.ams.org /ert/1997-001-14/S1088-4165-97-00020-4/home.html (357 words)

	Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 1, pp. 203-221, 2000 (Site not responding. Last check: 2007-10-13)
		Abstract: \font\frak=eufm10 \def\f#1{\hbox{\frak#1}} A quadratic Lie superalgebra is a Lie superalgebra ${\f g}={\f g}_{\bar 0}\oplus{\f g}_{\bar 1}$ with a non-degenerate, supersymmetric, even and ${\f g}$-invariant bilinear form $B$, $B$ is called an invariant scalar product of ${\f g}$.
		In this paper, we study properties of the decomposition of a quadratic Lie superalgebra ${\f g}={\f g}_{\bar 0}\oplus{\f g}_{\bar 1}$ relative to a fixed Cartan subalgebra of ${\f g}_{\bar 0}$.
		Finally, we give two characterizations of the basic classical Lie superalgebras among the quadratic Lie superalgebras.
	www.maths.tcd.ie /EMIS/journals/BAG/vol.41/no.1/18.html (161 words)

	Atlas: Nilpotent Lie superalgebras by Marc Gilg
		Nilpotent Lie superalgebras For a Lie superalgebra G over an algebraic closed field of carateristic 0 we define the lower central series C
		The set of filiform Lie superalgebras is an open set of the variety of nilpotent Lie superalgebras' laws.
		Classifications of filiforms over C in lower dimensions Using the bases of the cocycles and adapted chages of bases, like it was done for Lie algebras we have classifications of filiform Lie superalgebras.
	atlas-conferences.com /c/a/f/e/09.htm (220 words)

	New Page 1 (Site not responding. Last check: 2007-10-13)
		Shapovalov determinants of Q-type Lie superalgebras, preprint 2004, gzipped ps-file
		Kac's construction of the centre of $U(g)$ for Lie superalgebras, preprint 2003, gzipped ps-file
		On the ghost centre of Lie superalgebras, Annales Institut Fourier, t.
	www.wisdom.weizmann.ac.il /~/gorelik/publications.htm (168 words)

	References on Superalgebras
		ON PRINCIPAL SUBALGEBRAS OF LIE SUPERALGEBRAS AND UNIMODALITY.
		THE REPRESENTATIONS OF THE SYMPLECTIC AND CONFORMAL SUPERALGEBRAS.
		CONSTRUCTION OF LIE ALGEBRAS AND LIE SUPERALGEBRAS FROM TERNARY ALGEBRAS.
	wwwlapp.in2p3.fr /~frappat/refsuper.html (5497 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Making use of a Howe duality involving the infinite-dimensional Lie superalgebra $\hgltwo$ and the finite-dimensional group $GL_l$ we derive a character formula for a certain class of irreducible quasi-finite representations of $\hgltwo$ in terms of hook Schur functions.
		We use the reduction procedure of $\hgltwo$ to $\hat{gl}_{nn}$ to derive a character formula for a certain class of level 1 highest weight irreducible representations of $\hat{gl}_{nn}$, the affine Lie superalgebra associated to the finite-dimensional Lie superalgebra $gl_{nn}$.
		We also show that the characters of all integrable level 1 highest weight irreducible $\hat{gl}_{mn}$-modules may be written as a sum of products of hook Schur functions.
	celestial.eprints.org /cgi-bin/oaia2/arXiv.org?verb=GetRecord&identifier=oai:arXiv.org:math/0206034&metadataPrefix=oai_dc (118 words)

	Sophus Lie 2004/1
		In particular, subjects of interest are Lie algebras, Lie groups, Lie semigroups, homogeneous spaces and their geometry, applications of Lie theory to the theory of differential equations, symmetries...
		A class of Z_2-gaded Lie algebra and Lie superalgebra extensions of the pseudo-orthogonal algebra of a spacetime of arbitrary dimension and signature is investigated.
		We treat the connected almost differentiable left A-loops as images of global differentiable sharply transitive sections $\sigma :G/H \to G$ for a Lie group $G$ with the properties $\sigma(H)=1 \in G$ and $\sigma (G/H)$ generates $G$ such that the subset $\sigma (G/H)$ is invariant under the conjugation with the elements of $H$.
	www.boku.ac.at /math/SSL2004/sl2004.html (1420 words)

	Math arXiv: Search results (Site not responding. Last check: 2007-10-13)
		hep-th/0602169 Representations of the Lie Superalgebra gl(1n) in a Gel'fand-Zetlin Basis and Wigner Quantum Oscillators.
		math-ph/0511058 Lie superalgebraic framework for generalization of quantum statistics.
		q-alg/9507026 Unitarizable Representations of the Deformed Para-Bose Superalgebra Uq[osp(1/2)] at Roots of 1.
	front.math.ucdavis.edu /author/Stoilova-N* (364 words)

	DC MetaData for: Representations of the Exceptional Lie Superalgebra E(3,6): I.~Degeneracy Conditions. (Site not responding. Last check: 2007-10-13)
		DC MetaData for: Representations of the Exceptional Lie Superalgebra E(3,6): I.~Degeneracy Conditions.
		Representations of the Exceptional Lie Superalgebra E(3,6): I.~Degeneracy Conditions.
		extends the well-known classification of E.~Cartan in the Lie
	www.esi.ac.at /Preprint-shadows/esi921.html (95 words)

	Maria Gorelik at MSRI - The centre of P-type Lie superalgebra (Site not responding. Last check: 2007-10-13)
		Maria Gorelik at MSRI - The centre of P-type Lie superalgebra
		Maria Gorelik - The centre of P-type Lie superalgebra
		A PDF version of the lecture notes is available here.
	www.msri.org /publications/ln/msri/2002/ssymmetry/gorelik/1 (30 words)

	Abstract of Vaintrob's Talk (Site not responding. Last check: 2007-10-13)
		It is known that the Alexander-Conway knot polynomial is the Kontsevich integral applied to weight systems coming from the Lie superalgebra $gl(11)$.
		We show that the corresponding link invariant is related to the multi- variable Alexander polynomial $\Delta$.
		Moreover, we show that Vassiliev invariants coming from any solvable Lie algebra (or Lie superalgebra) belong to the subalgebra generated this implies that the space of Vassiliev invariants coming from Lie superalgebras is strictly larger than from all Lie algebras with invariant inner product.
	www.math.columbia.edu /conf/birman/Vaintrob.html (101 words)

	Chemla: Poincaré duality for $k$-$A$ Lie superalgebras
		and#x2014; Open problems in representation theory of Lie groups, in Proceedings of the Eighteenth International Symposium, division of mathematics, the Taniguchi Foundation.
		and#x2014; Cohomology of infinite dimensional Lie algebras, Contemporary Soviet Mathematics,
		and#x2014; Graded manifolds, graded Lie theory and prequantization, Lecture Notes in Math., t.
	www.numdam.org /numdam-bin/item?id=BSMF_1994__122_3_371_0 (253 words)

	Math arXiv: Search results (Site not responding. Last check: 2007-10-13)
		math.RT/9811015 Characters and composition factor multiplicities for the Lie superalgebra gl(m/n).
		q-alg/9607010 Convolutions for orthogonal polynomials from Lie and quantum algebra representations.
		q-alg/9501020 The quantum superalgebra $U_q[osp(1/2n)]$: deformed para-Bose operators and root of unity representations.
	front.math.ucdavis.edu /author/Van-der-Jeugt-J* (383 words)

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