Year: 2011
Type: article
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 \documentclass[12pt]{minimal}\begin{document}$U_q(\mathfrak {g}) \otimes \mathrm{cl}_q(\mathfrak {g})$\end{document}Uq(g)⊗ cl q(g), where the second tensor factor is a q-deformation of the classical Clifford algebra. The tensor space \documentclass[12pt]{minimal}\begin{document}$U_q(\mathfrak {g}) \otimes \mathrm{cl}_q(\mathfrak {g})$\end{document}Uq(g)⊗ cl q(g) is given by 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 P. N. Bibikov and P. P. Kulish [J. Math. Sci. (N.Y.) 100, 2039–2050 (2000)].
Source: Journal of Mathematical Physics
DOI: 10.1063/1.3664284
Author: Antti J. Harju
Institution: University of Helsinki
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1985913530