TY - JOUR

T1 - On the diagonal subalgebra of an Ext algebra

AU - Green, E. L.

AU - Snashall, N.

AU - Solberg,

AU - Zacharia, D.

N1 - Publisher Copyright:
© 2016 The Author(s)
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jpaa.2016.08.007

DO - 10.1016/j.jpaa.2016.08.007

M3 - Article

AN - SCOPUS:84997287911

VL - 221

SP - 847

EP - 866

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 4

ER -