论文标题
在分裂的准海层封面和林吉尔二元性上
On split quasi-hereditary covers and Ringel duality
论文作者
论文摘要
在本文中，我们开发了两个相对于模块相对于模块的模块和相对统一维数，称为相对主导维度。这些用于在林格二元性，拆分准鞘层覆盖物和双中央式特性之间建立精确的连接。 这些同源不变的人是在赛车代数上研究的，这些代数是有限生成和投射为地面环上的模块的，并且证明它们在戒指技术的变化下表现很好。事实证明，相对于特征倾斜模块的汇总的相对指导维度是构造Noetherian代数的准遗传覆盖物并衡量其质量的有用工具。特别是，这种同源不变用于使用$ q $ -schur代数的林吉尔双重性来构建iWahori-hecke代数的拆分准式封面。将封面理论的技术与相对主导的维度理论相结合，我们获得了伯恩斯坦 - 吉尔夫德·吉尔夫德类别块的林吉尔自偶性$ \ mathcal {o} $的新证明。
In this paper, we develop two new homological invariants called relative dominant dimension with respect to a module and relative codominant dimension with respect to a module. These are used to establish precise connections between Ringel duality, split quasi-hereditary covers and double centraliser properties. These homological invariants are studied over Noetherian algebras which are finitely generated and projective as a module over the ground ring and they are shown to behave nicely under change of rings techniques. It turns out that relative codominant dimension with respect to a summand of a characteristic tilting module is a useful tool to construct quasi-hereditary covers of Noetherian algebras and measure their quality. In particular, this homological invariant is used to construct split quasi-hereditary covers of quotients of Iwahori-Hecke algebras using Ringel duality of $q$-Schur algebras. Combining techniques of cover theory with relative dominant dimension theory we obtain a new proof for Ringel self-duality of the blocks of the Bernstein-Gelfand-Gelfand category $\mathcal{O}$.
