Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771801 | Journal of Algebra | 2017 | 51 Pages |
Abstract
Let k be a field and let Î be a finite dimensional k-algebra. We prove that every bounded complex V
- of finitely generated Î-modules has a well-defined versal deformation ring R(Î,V
- ) which is a complete local commutative Noetherian k-algebra with residue field k. We also prove that nice two-sided tilting complexes between Î and another finite dimensional k-algebra Î preserve these versal deformation rings. Additionally, we investigate stable equivalences of Morita type between self-injective algebras in this context. We apply these results to the derived equivalence classes of the members of a particular family of algebras of dihedral type that were introduced by Erdmann and shown by Holm to be not derived equivalent to any block of a group algebra.
- of finitely generated Î-modules has a well-defined versal deformation ring R(Î,V
- ) which is a complete local commutative Noetherian k-algebra with residue field k. We also prove that nice two-sided tilting complexes between Î and another finite dimensional k-algebra Î preserve these versal deformation rings. Additionally, we investigate stable equivalences of Morita type between self-injective algebras in this context. We apply these results to the derived equivalence classes of the members of a particular family of algebras of dihedral type that were introduced by Erdmann and shown by Holm to be not derived equivalent to any block of a group algebra.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Frauke M. Bleher, José A. Vélez-Marulanda,