Journal of Noncommutative Geometry


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Volume 1, Issue 3, 2007, pp. 281–309
DOI: 10.4171/JNCG/8

Published online: 2007-09-30

The first Hochschild cohomology group of quantum matrices and the quantum special linear group

Stéphane Launois[1] and Thomas H. Lenagan[2]

(1) University of Kent, Canterbury, Kent, UK
(2) University of Edinburgh

We calculate the first Hochschild cohomology group of quantum matrices, the quantum general linear group and the quantum special linear group in the generic case when the deformation parameter is not a root of unity. As a corollary, we obtain information about twisted Hochschild homology of these algebras.

Keywords: Quantum matrices, quantum special linear group, derivation, Hochschild cohomology, twisted Hochschild homology

Launois Stéphane, Lenagan Thomas: The first Hochschild cohomology group of quantum matrices and the quantum special linear group. J. Noncommut. Geom. 1 (2007), 281-309. doi: 10.4171/JNCG/8