On blocks of defect two and one simple module, and Lie algebra structure of HH¹

Benson, D. J., Kessar, R. & Linckelmann, M. (2017). On blocks of defect two and one simple module, and Lie algebra structure of HH¹. Journal of Pure and Applied Algebra, doi: 10.1016/j.jpaa.2017.02.010

Abstract

Let k be a field of odd prime characteristic p. We calculate the Lie algebra structure of the first Hochschild cohomology of a class of quantum complete intersections over k. As a consequence, we prove that if B is a defect 2-block of a finite group algebra $kG$ whose Brauer correspondent C has a unique isomorphism class of simple modules, then a basic algebra of B is a local algebra which can be generated by at most 2√I elements, where I is the inertial index of B, and where we assume that k is a splitting field for B and C.

Publication Type:	Article
Additional Information:	© 2017, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	math.RT; math.RT; math.GR; 20C20
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics