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Mat. Zametki, 2009, Volume 86, Issue 5, Pages 705–724 (Mi mz8514)  

This article is cited in 4 scientific papers (total in 4 papers)

Algebras with Periodic Shifts of Ext Degrees

Lu Jiafeng

Zhejiang Normal University

Abstract: The so-called $\lambda$-Koszul algebra and $\lambda$-Koszul module are introduced. We give different equivalent descriptions of a $\lambda$-Koszul algebra in terms of its minimal graded projective resolution and the Yoneda $\operatorname{Ext}$-algebra $E(A)=\bigoplus_{i\ge 0}\operatorname{Ext}^i_A(\mathbb F,\mathbb F)$. 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 $\operatorname{Ext}$-algebra of a $\lambda$-Koszul algebra.

Keywords: $\lambda$-Koszul algebras (modules), (strongly) weakly $\lambda$-Koszul, Yoneda $\operatorname{Ext}$-algebras, $A_{\infty}$-algebras, Lie algebra, module over a graded algebra

DOI: https://doi.org/10.4213/mzm8514

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English version:
Mathematical Notes, 2009, 86:5, 665–681

Bibliographic databases:

UDC: 512.54
Received: 19.07.2007
Revised: 16.09.2008

Citation: Lu Jiafeng, “Algebras with Periodic Shifts of Ext Degrees”, Mat. Zametki, 86:5 (2009), 705–724; Math. Notes, 86:5 (2009), 665–681

Citation in format AMSBIB
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\by Lu Jiafeng
\paper Algebras with Periodic Shifts of Ext Degrees
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\yr 2009
\vol 86
\issue 5
\pages 705--724
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\transl
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\vol 86
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\pages 665--681
\crossref{https://doi.org/10.1134/S0001434609110091}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Lü Jiafeng, Zhao Zhibing, “Quasi-$d$-Koszul modules and applications”, Chin. Ann. Math. Ser. B, 31:4 (2010), 481–490  crossref  mathscinet  zmath  isi  scopus
    2. Chen P.-S., Lue J.-F., “New Criteria for Lambda-Koszul Algebras”, Indian J. Pure Appl. Math., 42:3 (2011), 157–172  crossref  mathscinet  zmath  isi  scopus
    3. Lü Jia-Feng, “Koszul-Like Algebras and Modules”, Math. Notes, 93:3 (2013), 431–450  mathnet  crossref  crossref  mathscinet  isi  elib
    4. Lu J.-F., “(a, B, C)-Koszul Algebras”, Bull. Malays. Math. Sci. Soc., 36:2 (2013), 447–463  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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