P-Adic lifting problems and derived equivalences

Eisele, F. (2012). P-Adic lifting problems and derived equivalences. Journal of Algebra, 356(1), pp. 90-114. doi: 10.1016/j.jalgebra.2012.01.015

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Abstract

For two derived equivalent k-algebras λ̄ and γ̄, we introduce a correspondence between O-orders reducing to λ̄ and O-orders reducing to γ̄. We outline how this may be used to transfer properties like uniqueness (or non-existence) of a lift between λ̄ and γ̄. As an application, we look at tame algebras of dihedral type with two simple modules, where, most notably, we are able to show that among those algebras only the algebras Dκ,0(2A) and Dκ,0(2B) can actually occur as basic algebras of blocks of group rings of finite groups.

Item Type: Article
Additional Information: © 2012, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords: Orders; Integral representations; Derived equivalences; Dihedral defect
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/13179

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