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)
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.
UR - http://www.scopus.com/inward/record.url?scp=84997287911&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84997287911&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2016.08.007
DO - 10.1016/j.jpaa.2016.08.007
M3 - Article
AN - SCOPUS:84997287911
SN - 0022-4049
VL - 221
SP - 847
EP - 866
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 4
ER -