On the diagonal subalgebra of an Ext algebra

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• 作者：E.L. Green^a ; ^{green@math.vt.edu} ; N. Snashall^b ; ¹ ; ^{njs5@le.ac.uk} ; Ø ; . Solberg^c ; ² ; ^{oyvinso@math.ntnu.no} ; D. Zacharia^d ; ³ ; ^{zacharia@syr.edu}
• 关键词：Primary ; 16E30 ; secondary ; 16E40 ; 16S37
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：221
• 期：4
• 页码：847-866
• 全文大小：465 K
• 卷排序：221

文摘

Let R   be a Koszul algebra over a field kk and M be a linear R  -module. We study a graded subalgebra ΔMΔM 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 ΔRΔR 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.