Idempotents and homology of diagram algebras
Idempotents and homology of diagram algebras
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图代数的幂等性和同调性
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发表时间：
2022
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通讯作者：
Guy Boyde
中科院分区：
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作者：
Guy Boyde
.本文对代数同调的一些最新结果进行了系统化。我们的主要定理给出了一个图代数的同调同构于具有最大左到右连接数的图上的子代数的同调的判据。从这个定理出发，我们推出了Boeon-Hepworth和Boeon-Hepworth-Patzt的Temperley-Lieb和Brauer结果的“可逆参数”情形.我们也能够给一个新的证明Sroka定理的同源性的奇数股Temperley-Lieb代数消失，以及一个类似的结果Brauer代数和解释这两个结果在偶数股的情况下。我们的证明是相对初级的：特别是，不需要辅助链复合物或谱序列。本文布里讨论了它与Graham-Lehrer意义下的胞腔代数的关系。
. This paper provides a systematization of some recent results in homology of algebras. Our main theorem gives crite-ria 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.