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Title: On the diagonal subalgebra of an Ext algebra
Authors: Green, E. L.
Snashall, Nicole Jane
Solberg, O.
Zacharia, D.
First Published: 21-Aug-2016
Publisher: Elsevier on behalf of North-Holland Publishing
Citation: Journal of Pure and Applied Algebra, 2017, 221 (4), pp. 847-866
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.
DOI Link: 10.1016/j.jpaa.2016.08.007
ISSN: 0022-4049
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the authors, 2016. This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License (, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Appears in Collections:Published Articles, Dept. of Mathematics

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