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arXiv · 1009.3913

Covariant Dirac Operators on Quantum Groups

Antti J. Harju
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Abstract

We give a construction of a Dirac operator on a quantum group based on any simple Lie algebra of classical type. The Dirac operator is an element in the vector space $U_q(\g) \otimes \mathrm{cl}_q(\g)$ where the second tensor factor is a $q$-deformation of the classical Clifford algebra. The tensor space $ U_q(\g) \otimes \mathrm{cl}_q(\g)$ is given a structure of the adjoint module of the quantum group and the Dirac operator is invariant under this action. The purpose of this approach is to construct equivariant Fredholm modules and $K$-homology cycles. This work generalizes the operator introduced by Bibikov and Kulish in \cite{BK}.

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BibTeXRIS

Antti J. Harju. 2011-06-09. Covariant Dirac Operators on Quantum Groups. https://doi.org/10.1063/1.3664284

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