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Topic: Algebra representation of a Lie superalgebra

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	Springer Online Reference Works (Site not responding. Last check: 2007-11-05)
		Algebraic group, which to a significant extent absorbs it and extremely outgrows it, or in the theory of finite groups, cf.
		The theory of Lie algebras for this case is in the process of being established, and in a curious way it reflects the features of two different classes of complex Lie algebras, finite-dimensional simple algebras and finite-dimensional transitive simple algebras corresponding to primitive Lie pseudo-groups (see [17],, [19]).
		Infinite-dimensional graded Lie algebras are the subject of intensive research in which connections of these Lie algebras not only with classical geometrical questions but also with many other branches of mathematics have been discovered (see Lie algebra, graded, and also [17],, [22]).
	eom.springer.de /l/l058370.htm (2130 words)

	Algebra representation of a Lie superalgebra (Site not responding. Last check: 2007-11-05)
		Now, for the case of a representation of a Lie algebra, we simply drop all the gradings and the (-1) to the some power factors.
		A Lie (super)algebra is an Algebra and it also happens to be an adjoint representation of itself.
		This is a special case of an algebra representation of a Hopf algebra.
	algebra-representation-of-a-lie-superalgebra.mindbit.com (200 words)

	Encyclopedia :: encyclopedia : Abstract algebra (via CobWeb/3.1 planetlab1.netlab.uky.edu) (Site not responding. Last check: 2007-11-05)
		Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields.
		The term abstract algebra is used to distinguish the field from "elementary algebra" or "high school algebra", which teach the correct rules for manipulating formulas and algebraic expressions involving real and complex numbers, and unknowns.
		Historically, algebraic structures usually arose first in some other field of mathematics, were specified axiomatically, and were then studied in their own right in abstract algebra.
	www.hallencyclopedia.com.cob-web.org:8888 /topic/Abstract_algebra.html (281 words)

	Schur duality for the Cartan type Lie algebra (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		Introduction Cartan type Lie algebras are Lie subalgebras of algebraic vector fields on a flat affine space F n, where F is a field of...
		1 The irreducible representations of a semigroup related to th..
		1 Commutant algebra and harmonic polynomials of a Lie algebra..
	citeseer.ist.psu.edu /nishiyama99schur.html (319 words)

	Representation of a Lie algebra - Wikipedia, the free encyclopedia
		In mathematics, a representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator.
		Roughly speaking, the representations of Lie algebras are the differentiated form of representations of Lie groups, while the representations of the universal cover of a Lie group are the integrated form of the representations of its Lie algebra.
		Representations of a Lie algebra are in one-to-one correspondence with representations of the associated universal enveloping algebra.
	en.wikipedia.org /wiki/Representation_of_Lie_algebras (449 words)

	Chanyoung Shader
		algebras, and thus to construct representations and to describe their characters explicitly in terms of combinatorial tools and algorithms.
		Unlike for the representations of the classical Lie algebras and their guantum groups, the representations of Lie superalgebras and their quantum groups are not completely reducible in general.
		Lee Shader, Representations of Lie superalgebras of type C, to appear in J. Algebra.
	math.uwyo.edu /Prof_home/Shader_C.html (478 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-11-05)
		The formula is a generalization of Weyl's classical formula for the character of an irreducible finite-dimensional representation of a semi-simple Lie algebra (cf.
		The formula is very robust and has been steadily applied (with increasing technical complications) to the representations of ever wider classes of algebras, see [a3] for representations of Kac–Moody algebras and [a2] for generalized Kac–Moody (or Borcherds) algebras.
		These character formulas may also be applied to representations of associated quantum groups where quantum deformation theorems are known (see [a4] and [a1], for example).
	eom.springer.de /w/w130070.htm (267 words)

	Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture, Tomoyuki Arakawa
		Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture, Tomoyuki Arakawa
		Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture
		We study the representation theory of the superconformal algebra $\mathcal{W}_k(\mathfrak{g},f_{\theta})$ associated with a minimal gradation of $\frak{g}$.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.dmj/1133447439 (540 words)

	Supersymmetry - ExampleProblems.com (Site not responding. Last check: 2007-11-05)
		Traditional symmetries in physics are generated by objects that transform under the various tensor representations of the Poincaré group.
		Unique up to isomorphism, this Lie group is canonically associated with the Lie algebra, and the algebra's representations can be extended to create group representations.
		In the same way, representations of a Lie superalgebra can sometimes be extended into representations of a Lie supergroup.
	www.exampleproblems.com /wiki/index.php/Supersymmetry (2426 words)

	Ian M. Musson: Papers/Preprints
		We show there is a surjective homomorphism from $U(\FRAK{g})$ to the $r^{th}$ Weyl algebra $A_{r}$, and use this to construct an analog of the Joseph ideal.
		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 ${\mathfrak g}$.
		Abstract: Let $H_{\mathbf{k}}$ be a symplectic reflection algebra corresponding to a cyclic subgroup $\Gamma \subseteq SL_2 \C$ oforder $n$ and $U_{\mathbf{k}} = eH_{\mathbf{k}} e$ the spherical subalgebra of $H_{\mathbf{k}}$.
	www.uwm.edu /~musson/preprints.html (1159 words)

	Workshop on Representation Theory and Geometry 2005
		A crucial role in the theory of SRA associated with wreath-productsis is a construction of these algebras by means of quantum Hamiltonian reduction.
		To study the representation theory of U, Drinfeld used the KZ-equations to construct a quasi-Hopf algebra A. He proved that particular categories of modules over the algebras U and A are tensor equivalent.
		This modification is dictated by the representation theory of the double affine Hecke algebra.
	math.berkeley.edu /~bwebste/workshop2005.html (999 words)

	Benkart (Site not responding. Last check: 2007-11-05)
		Her main research interests are Lie algebras and groups, representation theory, and combinatorics.
		She has been a contributor to the classification of simple Lie algebras of prime characteristic and of infinite-dimensional Lie algebras ([1-3]) and to combinatorial representation theory ([4-5]).
		She has been an editor of Journal of Algebra since 1991 and serves on the editorial board of the AMS' Surveys and Monographs series.
	www.maa.org /sections/Benkart.htm (312 words)

	Crystal
		I am studying representation theory of infinite dimensional Lie (super)algebras.
		I am visiting the Weizmann Institute in Israel this fall, and I spoke in their algebra seminar on June 21, 2006.
		Contragredient Lie superalgebras of finite growth, Weizmann Institute of Science, Israel, Representation Theory Seminar, June 21, 2006.
	math.berkeley.edu /~crystal (396 words)

	Joerg's talks
		The graded Lie superalgebra structure on the Hochschild cohomology of truncated polynomial algebras
		Lie Algebras, Vertex Operator Algebras and their Applications, A Conference in Honor of Robert Lee Wilson and James Lepowsky on their 60th Birthdays, North Carolina State University, Raleigh, North Carolina
		Conference on the Structure and Representation Theory of Lie Algebras in Honor of the 60th Birthday of Professor George B. Seligman, Yale University, New Haven, Connecticut
	www.southalabama.edu /mathstat/personal_pages/feldvoss/talks.html (1097 words)

	ALGEBRAIC definition of ALGEBRAIC in computing dictionary - by the Free Online Dictionary, Thesaurus and Encyclopedia. ... (Site not responding. Last check: 2007-11-05)
		algebraic - In domain theory, a complete partial order is algebraic if every element is the least upper bound of some chain of compact elements.
		If the set of compact elements is countable it is called omega-algebraic.
		This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.
	computing-dictionary.thefreedictionary.com.cob-web.org:8888 /ALGEBRAIC (113 words)

	MIT - Math Department - Infinite-Dimensional Algebra Seminar (Site not responding. Last check: 2007-11-05)
		This algebra is a deformation Hopf algebra defined by generators and relations.
		The main idea is to synthesize the algebraic approach to the classical equivariant cohomology theory due to H.~Cartan and Guillemin--Sternberg, with the chiral de~Rham complex of Malikov--Schechtman--Vaintrob, by using a vertex algebra notion of invariant theory.
		This category is equivalent to the module category over a certain finite dimension algebra which is canonically constructed.
	www-math.mit.edu /inf-dim (467 words)

	BRS charge - BRScharge
		The BRST theory is in fact linked to the standard resolution in Lie algebra cohomology.
		Although the BRST formalism is more general than the Faddeev-Popov gauge fixing, in the special case where it is derived from it, the BRST operator is also useful to obtain the right Jacobian associated with constraints that gauge-fix the symmetry.
		It generates the Lie superalgebra with a zero-dimensional even part and a one dimensional odd part spanned by Q. [Q,Q)={Q,Q}=0 where [,) is the Lie superbracket (i.e.
	www.kopete.org /BRS-charge.html (539 words)

	Unconventional Lie Algebras - (American Mathematical Society Bookstore) (Site not responding. Last check: 2007-11-05)
		Among the topics covered here are generalizations of the Virasoro algebra, representation theory of the Virasoro algebra and of Kac-Moody algebras, cohomology of Lie algebras of vector fields on the line, and Lie superalgebras of vector fields.
		The Lie algebras here are either infinite-dimensional, are defined over fields of finite characteristic, or are actually Lie superalgebras or quantum groups.
		Kozerenko -- Main theorems of invariant theory for the Lie algeb ra $\germ{sl}(2)$ in the case of a field of finite characteristic
	mirror.math.nankai.edu.cn /mirror/www.ams.org/ADVSOV-17.html (395 words)

	AMCA: Quantized modules over basic Lie superalgebras by Nathan Geer (Site not responding. Last check: 2007-11-05)
		Analogous constructions of the algebras U and A exist for basic Lie superalgebras.
		Moreover, from this work, it follows that all highest weight modules of a basic Lie superalgebra can be deformed to modules over the Drinfeld-Jimbo type 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/q/i/45.htm (208 words)

	IngentaConnect On representations of the Lie superalgebra p(n)
		We introduce a new way to study representations of the Lie superalgebra p(n).
		Since the center of the universal enveloping algebra U acts trivially on all irreducible representations, we suggest to study the quotient algebra\overline{{U}}by the radical of U. We show that\overline{{U}}has a large center which separates typical finite-dimensional irreducible representations.
		Using this description we obtain character formulae of generic (infinite-dimensional) irreducible representations.
	www.ingentaconnect.com /content/ap/ja/2002/00000258/00000002/art00645 (151 words)

	Math arXiv: Search results (Site not responding. Last check: 2007-11-05)
		math.KT/0404139 Lie superalgebra structures in cohomology spaces of Lie algebras with coefficients in the adjoint representation.
		math.OA/0209040 On the structure of Banach algebras associated with automorphisms.
		math.OA/0209039 On the structure of Banach algebras associated with automorphisms.
	front.math.ucdavis.edu /author/Lebedev-A* (221 words)

	Prof. Li Liao's publication
		Li Liao & Xing-Chang Song, "q-Deformation of Lie Superalgebra B(m,n), B(0,n), C(1+n) and D(m,n) in Their Boson-Fermion Representation", Journal of Physics, A24(1991)5451-5463.
		Li Liao & Xing-Chang Song, "Spinor and Oscillator Representations of Quantum Enveloping Algebras of Type B_n, C_n and D_n", Commun.
		Li Liao & Xing-Chang Song, "On q-Differential Representation of Quantum Lie Superalgebras", ICTP Preprint, IC/94/7, Trieste, Italy.
	www.eecis.udel.edu /~lliao/publist.html (801 words)

	AMCA: Workshop and Conference on Infinite Dimensional Lie Theory and Its Applications - List of Speakers (Site not responding. Last check: 2007-11-05)
		Ana Duff Central extensions of the elementary unitary Lie superalgebra
		Geoffrey Mason Discrete series of the Virasoro algebra and the smallest conformal field theories
		Robert Wendt On representations of non-connected loop groups
	at.yorku.ca /c/a/l/s/01.htm (225 words)

	BRST formalism (via CobWeb/3.1 planetlab1.netlab.uky.edu) (Site not responding. Last check: 2007-11-05)
		The BRST theory is in fact linked to the standard resolution in Lie algebra cohomology.
		It generates the Lie superalgebra with a zero-dimensional even part and a one dimensional odd part spanned by Q. [Q,Q)={Q,Q}=0 where [,) is the Lie superbracket (i.e.
		are the infinitesimal generators of the Lie group, and f
	www.e-tv.co.za.cob-web.org:8888 /b/r/s/BRST_formalism_128b.html (545 words)

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