Deformations of complexes for finite dimensional algebras

Frauke M. Bleher, Jose A. Velez-Marulanda

Published 2015-11-25Version 1

Let $k$ be a field and let $\Lambda$ be a finite dimensional $k$-algebra. We prove that every bounded complex $V^\bullet$ of finitely generated $\Lambda$-modules has a well-defined versal deformation ring $R(\Lambda,V^\bullet)$ which is a complete local commutative Noetherian $k$-algebra with residue field $k$. We also prove that certain nice two-sided tilting complexes between $\Lambda$ and another finite dimensional $k$-algebra $\Gamma$ preserve these versal deformation rings. We apply these results to the derived equivalence class of a particular family of algebras of dihedral type which were introduced by Erdmann and shown by Holm to be not derived equivalent to any block of a group algebra.