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Equivalence of certain categories of modules for quantized affine lie algebras

Part of: Lie algebras and Lie superalgebras Groups and algebras in quantum theory

Published online by Cambridge University Press:  09 April 2009

Vyacheslav M. Futorny  and
Duncan J. Melville
Vyacheslav M. Futorny
Affiliation:
Instituto de Matematica Universidade do Sao PauloSao PauloBrasil e-mail: futorny@ime.usp.br
Duncan J. Melville
Affiliation:
Department of Mathematics St. Lawrence University Canton, New York 13617USA e-mail: dmel@music.stlawu.edu
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Abstract

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We show that a quantum Verma-type module for a quantum group associated to an affine Kac-Moody algebra is characterized by its subspace of finite-dimensional weight spaces. In order to do this we prove an explicit equivalence of categories between a certain category containing the quantum Verma modules and a category of modules for a subalgebra of the quantum group for which the finite part of the Verma module is itself a module.

MSC classification

Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 81R50: Quantum groups and related algebraic methods
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 2 , October 2000 , pp. 162 - 175
Copyright
Copyright © Australian Mathematical Society 2000

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