On the diagonal subalgebra of an Ext algebra

E. L. Green, N. Snashall, Solberg, D. Zacharia

Research output: Contribution to journalArticle

Abstract

Let R be a Koszul algebra over a field k and M be a linear R-module. We study a graded subalgebra ΔM of the Ext-algebra ExtR(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 ΔR is isomorphic to the graded center of the Koszul dual of R. When R is selfinjective and not necessarily graded, we study connections between periodic modules M, complexity of M and existence of non-nilpotent elements of positive degree in the Ext-algebra of M. Characterizations of periodic algebras are given.

Original languageEnglish (US)
Pages (from-to)847-866
Number of pages20
JournalJournal of Pure and Applied Algebra
Volume221
Issue number4
DOIs
StatePublished - Apr 1 2017

ASJC Scopus subject areas

  • Algebra and Number Theory

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