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)

Abstract

For two derived equivalent k-algebras Λ and Γ , we introduce a correspondence between O-orders reducing to Λ and O-orders reducing to Γ . We outline how this may be used to transfer properties like uniqueness (or non-existence) of a lift between Λ and Γ . 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: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Eisele, Dr Florian
• Authors: Eisele, F.
• College/School: College of Science and Engineering > School of Mathematics and Statistics
• Journal Name: Journal of Algebra
• Publisher: Elsevier
• ISSN: 0021-8693
• ISSN (Online): 1090-266X
• Published Online: 09 February 2012