论文标题
Jordan在温和代数上的一些模块子类别的可恢复性
Jordan recoverability of some subcategories of modules over gentle algebras
论文作者
论文摘要
温和的代数形成了1980年代由I. Ression和A.Skowroński引入的一类有限维代数。该代数上的模块可以通过M.C.R.的工作中相关的柔和颤抖中的弦和频带组合来描述。巴特勒和C.M.林吉尔。任何模块都可以自然与箭量表示。颤抖表示的nilpotent内态性诱导每个顶点的向量空间上的线性变换。通常，在所有尼尔胸内的内态性中，这些表示形式都有明确的约旦形式。我们专注于柔和颤抖的所有不可分解的表示，包括固定的顶点，在其支撑中，包括固定的顶点。我们展示了顶点的特征，使该子类别的对象通过其通用的Jordan形式确定为同构。
Gentle algebras form a class of finite-dimensional algebras introduced by I. Assem and A. Skowroński in the 1980s. Modules over such an algebra can be described by string and band combinatorics in the associated gentle quiver from the work of M.C.R. Butler and C.M. Ringel. Any module can be naturally associated to a quiver representation. A nilpotent endomorphism of a quiver representation induces linear transformations over vector spaces at each vertex. Generically among all nilpotent endomorphisms, a well-defined Jordan form exists for these representations. We focus on subcategories additively generated by all the indecomposable representations of a gentle quiver, including a fixed vertex in their support. We show a characterization of the vertices such that the objects of this subcategory are determined up to isomorphism by their generic Jordan form.
