泛变形环与自内射Nakayama代数
Universal deformation rings and self-injective Nakayama algebras
摘要：
设$k$是一个域，$Λ$是一个不可分解的有限维$k$ -代数，使得$Λ$与$k$上的自内射分裂基本Nakayama代数之间存在Morita型稳定等价.我们证明了每个不可分解的可积生成的$Λ$ -模$V$都有一个泛变形环$R(Λ,V)$，并将$R(Λ,V)$明确地描述为$k$上的幂级数环的商环.这一结果特别适用于Brauer树代数，因此适用于具有循环亏群的有限群的$p$ -模块。
英文摘要：
Let $k$ be a field and let $Λ$ be an indecomposable finite dimensional $k$-algebra such that there is a stable equivalence of Morita type between $Λ$ and a self-injective split basic Nakayama algebra over $k$. We show that every indecomposable finitely generated $Λ$-module $V$ has a universal deformation ring $R(Λ,V)$ and we describe $R(Λ,V)$ explicitly as a quotient ring of a power series ring over $k$ in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to $p$-modular blocks of finite groups with cyclic defect groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
