论文标题
多项式生长的通用brauer树代数的模块的通用变形环
Universal deformation rings of modules for generalized Brauer tree algebras of polynomial growth
论文作者
论文摘要
令$ k $为任意字段，$λ$为$ k $ - 代数，$ v $为$λ$ - 模块。当它存在时，$ v $的通用变形环$ r（λ，v）$是$ k $ -Algebra，其本地同质形态为$ r $ r $ aparatize $ v $ of $ v $ to $ r \otimes_kλ$，其中$ r $是本地通勤的noeetherian $ k $ -algebra cum $ k $ k $ k $ k $ k $ k $ k $。与Brauer图代数一致的对称特殊双重代数可以看作是概括有限型$ p $ p $ - 模块化组代数的块。 Bleher和Wackwitz对具有有限表示类型的对称特殊双层代数的所有模块的通用变形环分类。在本文中，我们开始解决驯服案例。具体来说，令$λ$为任何1个居住的，对称的特殊双词代数。通过将$λ$视为通用的brauer树代数并利用派生的等价，我们将$λ$ -Modules $ v $的通用变形环与稳定的内态ring同构为$ k $。后者是自然的条件，因为它可以保证存在通用变形环$ r（λ，v）$。
Let $k$ be an arbitrary field, $Λ$ be a $k$-algebra and $V$ be a $Λ$-module. When it exists, the universal deformation ring $R(Λ,V)$ of $V$ is a $k$-algebra whose local homomorphisms to $R$ parametrize the lifts of $V$ up to $R\otimes_k Λ$, where $R$ is any complete, local commutative Noetherian $k$-algebra with residue field $k$. Symmetric special biserial algebras, which coincide with Brauer graph algebras, can be viewed as generalizing the blocks of finite type $p$-modular group algebras. Bleher and Wackwitz classified the universal deformation rings for all modules for symmetric special biserial algebras with finite representation type. In this paper, we begin to address the tame case. Specifically, let $Λ$ be any 1-domestic, symmetric special biserial algebra. By viewing $Λ$ as generalized Brauer tree algebras and making use of a derived equivalence, we classify the universal deformation rings for those $Λ$-modules $V$ with stable endomorphism ring isomorphic to $k$. The latter is a natural condition, since it guarantees the existence of the universal deformation ring $R(Λ,V)$.
