Journal article
Universal deformation rings of modules over Frobenius algebras
Journal of Algebra, Vol.367, pp.176-202
11/05/2009
DOI: 10.1016/j.jalgebra.2012.06.008
Abstract
J. Algebra 367 (2012), 176-202 Let $k$ be a field, and let $\Lambda$ be a finite dimensional $k$-algebra. We prove that if $\Lambda$ is a self-injective algebra, then every finitely generated $\Lambda$-module $V$ whose stable endomorphism ring is isomorphic to $k$ has a universal deformation ring $R(\Lambda,V)$ which is a complete local commutative Noetherian $k$-algebra with residue field $k$. If $\Lambda$ is also a Frobenius algebra, we show that $R(\Lambda,V)$ is stable under taking syzygies. We investigate a particular Frobenius algebra $\Lambda_0$ of dihedral type, as introduced by Erdmann, and we determine $R(\Lambda_0,V)$ for every finitely generated $\Lambda_0$-module $V$ whose stable endomorphism ring is isomorphic to $k$.
Details
- Title: Subtitle
- Universal deformation rings of modules over Frobenius algebras
- Creators
- Frauke M BleherJose A Velez-Marulanda
- Resource Type
- Journal article
- Publication Details
- Journal of Algebra, Vol.367, pp.176-202
- DOI
- 10.1016/j.jalgebra.2012.06.008
- ISSN
- 0021-8693
- eISSN
- 1090-266X
- Language
- English
- Date published
- 11/05/2009
- Academic Unit
- Mathematics
- Record Identifier
- 9983985976002771
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