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FAMILIES OF DIRAC OPERATORS AND QUANTUM AFFINE GROUPS

Part of: Groups and algebras in quantum theory Topological $K$-theory

Published online by Cambridge University Press:  31 May 2011

JOUKO MICKELSSON
JOUKO MICKELSSON*
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland Department of Theoretical Physics, Royal Institute of Technology, Stockholm, Sweden (email: jouko@kth.se)
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Abstract

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Twisted K-theory classes over compact Lie groups can be realized as families of Fredholm operators using the representation theory of loop groups. In this paper we show how to deform the Fredholm family in the sense of quantum groups. The family of Dirac-type operators is parametrized by vectors in the adjoint module for a quantum affine algebra and transforms covariantly under a central extension of the algebra.

Keywords

Dirac operatorquantum affine algebraK-theory

MSC classification

Secondary: 81R10: Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations 19L50: Twisted $K$-theory; differential $K$-theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 90 , Issue 2 , April 2011 , pp. 213 - 220
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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