Journal article
Deformations of complexes for finite dimensional algebras
Journal of algebra, Vol.491, pp.90-140
11/25/2015
DOI: 10.1016/j.jalgebra.2017.08.003
Abstract
J. Algebra 491 (2017), 90-140 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 nice two-sided tilting complexes between $\Lambda$ and another finite dimensional $k$-algebra $\Gamma$ 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.
Details
- Title: Subtitle
- Deformations of complexes for finite dimensional algebras
- Creators
- Frauke M BleherJose A Velez-Marulanda
- Resource Type
- Journal article
- Publication Details
- Journal of algebra, Vol.491, pp.90-140
- DOI
- 10.1016/j.jalgebra.2017.08.003
- ISSN
- 0021-8693
- eISSN
- 1090-266X
- Grant note
- DOI: 10.13039/100000001, name: NSF, award: DMS-1360621; DOI: 10.13039/100010085, name: Valdosta State University
- Language
- English
- Date published
- 11/25/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9983985980002771
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