论文标题
图表代数的基础和同源性
Idempotents and homology of diagram algebras
论文作者
论文摘要
本文对代数同源性的一些最新结果进行了系统化。我们的主要定理给出了图表代数的同源性的标准，与具有最大左右连接次数的图中的亚代词的同源性同构。从这个定理中，我们推断出Boyd-Hepworth和Boyd-Hepworth-Patzt的Temperley-Lieb和Brauer结果的“可逆参数”案例。我们还能够给出Sroka定理的新证明，即奇特的Temperley-Lieb代数的同源性消失，以及对Brauer代数的类似结果，并且对这两种解释都在偶然的情况下产生了解释。我们的证明是相对基本的：尤其是不需要辅助链复合物或光谱序列。我们在Graham-Lehrer的意义上简要讨论与细胞代数的关系。
This paper provides a systematization of some recent results in homology of algebras. Our main theorem gives criteria under which the homology of a diagram algebra is isomorphic to the homology of the subalgebra on diagrams having the maximum number of left-to-right connections. From this theorem, we deduce the `invertible-parameter' cases of the Temperley-Lieb and Brauer results of Boyd-Hepworth and Boyd-Hepworth-Patzt. We are also able to give a new proof of Sroka's theorem that the homology of an odd-strand Temperley-Lieb algebra vanishes, as well as an analogous result for Brauer algebras and an interpretation of both results in the even-strand case. Our proofs are relatively elementary: in particular, no auxiliary chain complexes or spectral sequences are required. We briefly discuss the relationship to cellular algebras in the sense of Graham-Lehrer.
