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Quantum Algebra papers — page 42

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Affine Algebras, Langlands Duality and Bethe Ansatz
We review various aspects of representation theory of affine algebras at the critical level, geometric Langlands correspondence, and Bethe ansatz in the Gaudin models. Geometric Langlands…
Edward FrenkelJun 5, 1995
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Links, Quantum Groups, and TQFT's
The Jones polynomial and the Kauffman bracket are constructed, and their relation with knot and link theory is described. The quantum groups and tangle functor formalisms for understanding these…
Stephen SawinJun 2, 1995
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On Vassiliev knot invariants induced from finite type 3-manifold invariants
We prove that the knot invariant induced by a Z-homology 3-sphere invariant of order ≤ k in Ohtsuki's sense, where k≥ 4, is of order ≤ k-2. The method developed in our…
Matt Greenwood, Xiao-Song LinJun 1, 1995
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Lie-Poisson Deformation of the Poincaré Algebra
We find a one parameter family of quadratic Poisson structures on R4× SL(2,C) which satisfies the property a) that it is preserved under the Lie-Poisson action of the Lorentz…
A. Stern, I. YakushinMay 25, 1995
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Non-Symmetric Macdonald's Polynomials
We extend the previous paper "Macdonald's evaluation ... and applications" to the non-symmetric polynomilas recently introduced by Macdonald (as difference counterparts of Opdam's…
Ivan CherednikMay 24, 1995
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On the quantization of Poisson brackets
In this paper we introduce two classes of Poisson brackets on algebras (or on sheaves of algebras). We call them locally free and nonsingular Poisson brackets. Using the Fedosov's method we prove…
J. DoninMay 24, 1995
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Killing Form on Quasitriangular Hopf Algebras and Quantum Lie Algebras
The basics of quasitriangular Hopf algebras and quantum Lie algebras are briefly reviewed, and it is shown that their properties allow the introduction of a Killing form. For quantum Lie algebras,…
Paul WattsMay 23, 1995
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Direct Sum Decompositions and Indecomposable TQFT's
The decomposition of an arbitrary axiomatic topological quantum field theory or TQFT into indecomposable theories is given. In particular, unitary TQFT's in arbitrary dimensions are shown to…
Stephen SawinMay 23, 1995
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Quantum Affine Algebras and Deformations of the Virasoro and W-algebras
We generalize some results concerning affine algebras at the critical level to the corresponding quantum algebras. In particular, we show that the Wakimoto realization provides a homomorphism of…
Edward Frenkel, Nikolai ReshetikhinMay 22, 1995
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Hopf algebroids and quantum groupoids
We introduce the notion of Hopf algebroids, in which neither the total algebras nor the base algebras are required to be commutative. We give a class of Hopf algebroids associated to module algebras…
Jiang-Hua LuMay 19, 1995
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Vector Fields on Quantum Groups
We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between…
Paolo Aschieri, Peter SchuppMay 18, 1995
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On Hopf algebras and the elimination theorem for free Lie algebras
The elimination theorem for free Lie algebras, a general principle which describes the structure of a free Lie algebra in terms of free Lie subalgebras, has been recently used by E. Jurisich to prove…
J. Lepowsky, R. L. WilsonMay 18, 1995
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Riemannian Geometry on Quantum Spaces
An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is…
Pei-Ming HoMay 17, 1995
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A theory of tensor products for module categories for a vertex operator algebra, III
This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category''…
Yi-Zhi Huang, James LepowskyMay 17, 1995
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Virasoro vertex operator algebras, the (nonmeromorphic) operator product expansion and the tensor product theory
In the references [HL1]--[HL5] and [H1], a theory of tensor products of modules for a vertex operator algebra is being developed. To use this theory, one first has to verify that the vertex operator…
Yi-Zhi HuangMay 17, 1995
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A theory of tensor products for module categories for a vertex operator algebra, IV
This is the fourth part of a series of papers developing a tensor product theory of modules for a vertex operator algebra. In this paper, We establish the associativity of P(z)-tensor products for…
Yi-Zhi HuangMay 17, 1995
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ISOq(3) and ISOq(2,1)
We prove the embedding of ISOq(3) ISUexq(2) and ISOq(2,1) ISLexq(2,R) as *-algebras and give a Hilbert space representation of ISUexq(2)
S. Sachse, R. WeixlerMay 17, 1995
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Deformations of Multiparameter Quantum gl(N)
Multiparameter quantum gl(N) is not a rigid structure. This paper defines an essential deformation as one that cannot be interpreted in terms of a similarity transformation, nor as a perturbation of…
C. Fronsdal, A. GalindoMay 16, 1995
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Deformations of quadratic algebras and the corresponding quantum semigroups
Let V be a finite dimensional vector space. Given a decomposition V V=in Ii, define n quadratic algebras (V, Jm) where Jm=i≠ m Ii. This decomposition defines…
J. Donin, S. ShniderMay 16, 1995
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Universal T-matrix for Twisted Quantum gl(N)
The Universal T-matrix is the capstone of the structure that consists of a quantum group and its dual, and the central object from which spring the T-matrices (monodromies) of all the associated…
Christian FronsdalMay 16, 1995
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On a q-analogue of the multiple gamma functions
A q-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.
Michitomo NishizawaMay 16, 1995
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Elliptic Algebras and Equivariant Elliptic Cohomology
In this paper we explain the parallelism in the classification of three different kinds of mathematical objects: (i) Classical r-matrices. (ii) Generalized cohomology theories that have Chern classes…
Victor Ginzburg, Mikhail Kapranov, Eric VasserotMay 16, 1995
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Cohomology of Quantum Groups
Lecture notes. Introduction to the cohomology of algebras, Lie algebras, Lie bialgebras and quantum groups. Contains a new derivation of the classification of classical r-matrices in terms of…
Christian FronsdalMay 15, 1995
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Harish-Chandra decomposition for zonal spherical functions of type An
This paper is devoted to homological treatment of Harish-Chandra decomposition for zonal spherical functions of type An.
A. Kazarnovski-KrolMay 11, 1995
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New Level-0 Action of Uq(sl2) on Level-1 Modules
A level-0 action of Uq(sl2) is defined on the sum of level-1 irreducible highest weight modules. With the aid of the affine Hecke algebras, this action is realized on the basis created…
M. Jimbo, R. Kedem, H. Konno et al.May 9, 1995
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