Benson, D. J., Kessar, R. and 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 2block 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 AttributionNonCommercialNoDerivatives 4.0 International http://creativecommons.org/licenses/byncnd/4.0/ 
Publisher Keywords:  math.RT; math.RT; math.GR; 20C20 
Subjects:  Q Science > QA Mathematics 
Departments:  School of Mathematics, Computer Science & Engineering > Mathematics 
URI:  http://openaccess.city.ac.uk/id/eprint/14551 

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