Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring

Eisele, F. ORCID: 0000-0001-8267-2094 (2016). Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring. Journal of Algebra, 456, pp. 294-322. doi: 10.1016/j.jalgebra.2016.03.010

Abstract

We show that two blocks of generalized quaternion defect with three simple modules over a sufficiently large 2-adic ring O are Morita-equivalent if and only if the corresponding blocks over the residue field of O are Morita-equivalent. As a corollary we show that any two blocks defined over O with three simple modules and the same generalized quaternion defect group are derived equivalent.

Publication Type:	Article
Additional Information:	© Elsevier 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	Modular representation theory, Orders, Integral representations, Tame blocks
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics