p-Adic Lifting Problems and Derived Equivalences

Abstract

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.

References in corpus (2)

• Degenerations for derived categories
• Universal deformation rings and dihedral blocks with two simple modules

Cited by in corpus (5)

• Universal deformation rings and dihedral blocks with two simple modules
• On Tate duality and a projective scalar property for symmetric algebras
• Universal deformation rings and tame blocks
• Brauer's generalized decomposition numbers and universal deformation rings
• The p-adic group ring of SL_2(p^f)