Graded self-injective algebras "are" trivial extensions

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For a positively graded artin algebra A = ⊕n ≥ 0 An we introduce its Beilinson algebra b (A). We prove that if A is well-graded self-injective, then the category of graded A-modules is equivalent to the category of graded modules over the trivial extension algebra T (b (A)). Consequently, there is a full exact embedding from the bounded derived category of b (A) into the stable category of graded modules over A; it is an equivalence if and only if the 0-th component algebra A0 has finite global dimension. © 2009 Elsevier Inc. All rights reserved.




Chen, X. W. (2009). Graded self-injective algebras “are” trivial extensions. Journal of Algebra, 322(7), 2601–2606.

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