Algebras with periodic shifts of Ext degrees. (English. Russian original) Zbl 1203.16009
Math. Notes 86, No. 5, 665-681 (2009); translation from Mat. Zametki 86, No. 5, 705-724 (2009).
Summary: The so-called \(\lambda\)-Koszul algebra and \(\lambda\)-Koszul module are introduced. We give different equivalent descriptions of the \(\lambda\)-Koszul algebra in terms of its minimal graded projective resolution and the Yoneda Ext-algebra \(E(A)=\bigoplus_{i\geq 0}\text{Ext}_A^i(\mathbb{F},\mathbb{F})\). The “\(\lambda\)-Koszulity” of a finitely generated graded module is discussed and the concepts of (strongly) weakly \(\lambda\)-Koszul module are introduced. Finally, we discuss the \(A_\infty\)-structure on the Yoneda Ext-algebra of a \(\lambda\)-Koszul algebra.
MSC:
| 16E30 | Homological functors on modules (Tor, Ext, etc.) in associative algebras |
| 16S37 | Quadratic and Koszul algebras |
| 16E05 | Syzygies, resolutions, complexes in associative algebras |
Keywords:
Koszul algebras; Koszul modules; Yoneda Ext-algebras; \(A_\infty\)-algebras; Lie algebras; modules over graded algebras; projective resolutionsReferences:
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