Edward L. Green, Nicole Snashall, Øyvind Solberg, Dan Zacharia
Abstract: Let $R$ be a Koszul algebra over a field $k$ and $M$ be a linear $R$-module. We study a graded subalgebra $\Delta_M$ of the Ext-algebra $\operatorname{Ext}_R^*(M,M)$ called the diagonal subalgebra and its properties. Applications to the Hochschild cohomology ring of $R$ and to periodicity of linear modules are given. Viewing $R$ as a linear module over its enveloping algebra, we also show that $\Delta_R$ is isomorphic to the graded center of the Koszul dual of $R$.
Journal: Journal of Pure and Applied Algebra, Volume 221, Issue 4, April 2017, Pages 847–866
DOI: 10.1016/j.jpaa.2016.08.007