Three algebras and three definitions of Koszulness

Abstract: Let $R$ be a standard graded commutative algebra over a field $k$, let $K$ be the Koszul complex on a minimal set of generators of the irrelevant ideal of $R$, and let $H$ be the homology of $K$. Recall that $R$ is said to be \textit{Koszul} if $k$ has a linear free resolution over $R$. We adapt this definition to apply to $K$ (viewed as a DG algebra) and then to $H$ (viewed as a bigraded algebra). We describe how these three Koszul properties transfer back and forth between the three algebras $R$, $K$, and $H$, and we give several examples of classes of algebras $R$ for which $H$ is Koszul.

commutative algebraalgebraic topologyquantum algebrarepresentation theory

Audience: researchers in the topic

DG methods in commutative algebra and representation theory

Series comments: Description: Online special session

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