2012/12/23 by José A. Vélez-Marulanda, Jose A. Velez-Marulanda, Velez-Marulanda, Jose A.
Mathematics · Physics and Astronomy · #16G10 \and 16G20 \and 20C20 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT #msc:16G10 #msc:16G20 #msc:20C20
paper · pdf · doi:10.48550/arxiv.1212.5754
arxiv created 2012/12/23 · openalex publication_date 2012/12/23 · arxiv updated 2012/12/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let \k be an algebraically closed field, let \A be a finite dimensional \k-algebra and let V be a \A-module with stable endomorphism ring isomorphic to \k. If \A is self-injective then V has a universal deformation ring R(\A,V), which is a complete local commutative Noetherian \k-algebra with residue field \k. Moreover, if Λ is also a Frobenius \k-algebra then R(\A,V) is stable under syzygies. We use these facts to determine the universal deformation rings of string \Ar-modules whose stable endomorphism ring isomorphic to \k, where \Ar is a symmetric special biserial \k-algebra that has quiver with relations depending on the four parameters r=(r0,r1,r2,k) with r0,r1,r2≥ 2 and k≥ 1.