Universal deformation rings of modules over Frobenius algebras

作者：Bleher Frauke M^*; Velez Marulanda Jose A

来源：Journal of Algebra, 2012, 367: 176-202.

DOI：10.1016/j.jalgebra.2012.06.008

• Universal deformation rings
• Frobenius algebras
• Stable endomorphism rings

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.

• 出版日期2012-10-1