论文标题
准鞘内结构的组合
Combinatorics of quasi-hereditary structures
论文作者
论文摘要
准遗传代数是Artin代数，以及其一组符合某些条件的简单模块的同构类别的部分顺序。在本文中，我们调查了给定代数上准栖息结构屈服的所有可能选择，特别是我们介绍和研究了我们所谓的Quasi-herepitary结构的poset。我们的技术涉及某些颤抖的分解和减少的动力。对于Dynkin类型$ \ Mathbb {a} $的路径代数，我们提供了其准式结构的完整分类。对于类型$ \ mathbb {d} $和$ \ mathbb {e} $，我们给出了准级结构数量的计数方法。在遗传发生率的代数的情况下，我们为其准单层结构的POSET提供了必要和充分的条件，使其成为晶格。
A quasi-hereditary algebra is an Artin algebra together with a partial order on its set of isomorphism classes of simple modules which satisfies certain conditions. In this article we investigate all the possible choices that yield to quasi-hereditary structures on a given algebra, in particular we introduce and study what we call the poset of quasi-hereditary structures. Our techniques involve certain quiver decompositions and idempotent reductions. For a path algebra of Dynkin type $\mathbb{A}$, we provide a full classification of its quasi-hereditary structures. For types $\mathbb{D}$ and $\mathbb{E}$, we give a counting method for the number of quasi-hereditary structures. In the case of a hereditary incidence algebra, we present a necessary and sufficient condition for its poset of quasi-hereditary structures to be a lattice.
