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.
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Stéphane Launois, Thomas H. Lenagan, The first Hochschild cohomology group of quantum matrices and the quantum special linear group. J. Noncommut. Geom. 1 (2007), no. 3, pp. 281–309DOI 10.4171/JNCG/8