On the diagonal subalgebra of an Ext algebra
Edward L. Green, Nicole Snashall, {\O}yvind Solberg, Dan Zacharia

TL;DR
This paper investigates the properties of the diagonal subalgebra of an Ext algebra for Koszul algebras, revealing its structure, applications to Hochschild cohomology, and its relation to the Koszul dual.
Contribution
It introduces and analyzes the diagonal subalgebra of Ext algebras for Koszul algebras, connecting it to Hochschild cohomology and the graded center of the Koszul dual.
Findings
The diagonal subalgebra $ riangle_M$ has specific algebraic properties.
$ riangle_R$ is isomorphic to the graded center of the Koszul dual of $R$.
Applications to Hochschild cohomology and module periodicity are established.
Abstract
Let be a Koszul algebra over a field and be a linear -module. We study a graded subalgebra of the Ext-algebra called the diagonal subalgebra and its properties. Applications to the Hochschild cohomology ring of and to periodicity of linear modules are given. Viewing as a linear module over its enveloping algebra, we also show that is isomorphic to the graded center of the Koszul dual of .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Commutative Algebra and Its Applications
