p-Adic Lifting Problems and Derived Equivalences

Details p-Adic Lifting Problems and Derived Equivalences p-Adic Lifting Problems and Derived Equivalences

2011-02-08

arxiv.org/abs/1102.1674v2

Mathematics

Representation Theory

Scientific paper

10.1016/j.jalgebra.2012.01.015

For two derived equivalent $k$-algebras $\bar\Lambda$ and $\bar\Gamma$, we introduce a correspondence between $\OO$-orders reducing to $\bar\Lambda$ and $\OO$-orders reducing to $\bar\Gamma$. We outline how this may be used to transfer properties like uniqueness (or non-existence) of a lift between $\bar\Lambda$ and $\bar\Gamma$. 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 $\mathcal D^{\kappa,0}(2A)$ and $\mathcal D^{\kappa,0}(2B)$ can actually occur as basic algebras of blocks of group rings of finite groups.

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