论文标题
同源系统和Bocses
Homological systems and bocses
论文作者
论文摘要
我们表明，直到莫里塔等效性，任何具有合适同源系统的有限维代数都可以接受确切的Borel子代数。这概括了Koenig，Külshammer和Ovsienko的定理，该定理持有Quasi-Herseditary代数。我们的证明遵循了这些作者在更一般的环境中提出的相同的一般计划：我们使用$ a _ {\ infty}的结构将差异分级的张量代数与关系相关联 - $ a {\ infty} - $代数的$ ngebra，是合适的yoneda代数的$代数，并使用其模块类别使用其相关模量的类别来描述给定的家用系统的类别。
We show that, up to Morita equivalence, any finite-dimensional algebra with a suitable homological system, admits an exact Borel subalgebra. This generalizes a theorem by Koenig, Külshammer and Ovsienko, which holds for quasi-hereditary algebras. Our proof follows the same general scheme proposed by these authors, in a more general context: we associate a differential graded tensor algebra with relations, using the structure of $A_{\infty}-$algebra of a suitable Yoneda algebra, and use its category of modules to describe the category of filtered modules associated to the given homological system.
