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Keywords = DG skew polynomial algebra

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46 pages, 462 KiB  
Article
Cohomology Algebras of a Family of DG Skew Polynomial Algebras
by Xuefeng Mao and Gui Ren
Mathematics 2023, 11(7), 1617; https://doi.org/10.3390/math11071617 - 27 Mar 2023
Cited by 1 | Viewed by 2115
Abstract
Let A be a connected cochain DG algebra such that its underlying graded algebra A# is the graded skew polynomial algebra [...] Read more.
Let A be a connected cochain DG algebra such that its underlying graded algebra A# is the graded skew polynomial algebra kx1,x2,x3/x1x2+x2x1x2x3+x3x2x3x1+x1x3,|x1|=|x2|=|x3|=1. Then the differential A is determined by A(x1)A(x2)A(x3)=Mx12x22x32 for some MM3(k). When the rank r(M) of M belongs to {1,2,3}, we compute H(A) case by case. The computational results in this paper give substantial support for the research of the various homological properties of such DG algebras. We find some examples, which indicate that the cohomology graded algebras of such kind of DG algebras may be not left (right) Gorenstein. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics, 4th Edition)
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