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- W4297755751 abstract "Gelfand, Retakh, Serconek and Wilson, in cite{GRSW}, defined a graded algebra $A_Gamma$ attached to any finite ranked poset $Gamma$ - a generalization of the universal algebra of pseudo-roots of noncommutative polynomials. This algebra has since come to be known as the splitting algebra of $Gamma$. The splitting algebra has a secondary filtration related to the rank function on the poset and the associated graded algebra is denoted here by $A'_Gamma$. We calculate the cohomology algebra (and coalgebra) of $A'_Gamma$ explicitly. As a corollary to this calculation we have a proof that $A'_Gamma$ is Koszul (respectively quadratic) if and only if $Gamma$ is Cohen-Macaulay (respectively uniform). We show by example that the cohomology algebra (resp. coalgebra) of $A_Gamma$ may be strictly smaller that the cohomology algebra (resp. coalgebra) of $A'_Gamma$." @default.
- W4297755751 created "2022-10-01" @default.
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- W4297755751 date "2012-08-10" @default.
- W4297755751 modified "2023-09-25" @default.
- W4297755751 title "Splitting Algebras II: The Cohomology Algebra" @default.
- W4297755751 doi "https://doi.org/10.48550/arxiv.1208.2202" @default.
- W4297755751 hasPublicationYear "2012" @default.
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