Singular deformation theory and the invariance of Gerstenhaber algebra structure on the singular Hochschild cohomology

Zhengfang Wang

Published 2016-01-07Version 1

Keller proved in 1999 that the Gerstenhaber algebra structure of the Hochschild cohomology of an algebra is an invariant of the derived category. In this paper, we adapt his approach and develop the singular infinitesimal deformation theory. As a consequence, we show that the Gerstenhaber algebra structure on the singular Hochschild cohomology of an algebra is preserved under singular equivalences of Morita type with level.