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Mat. Zametki, 2013, Volume 93, Issue 3, Pages 413–435 (Mi mz10166)  

Koszul-Like Algebras and Modules

Lü Jia-Feng

Zhejiang Normal University

Abstract: In this paper, the notion of Koszul-like algebra is introduced; this notion generalizes the notion of Koszul algebra and includes some Artin–Schelter regular algebras of global dimension $5$ as special examples. Basic properties of Koszul-like modules are discussed. In particular, some necessary and sufficient conditions for $\mathcal{KL}(A)=\mathcal{L}(A)$ are provided, where $\mathcal{KL}(A)$ and $\mathcal{L}(A)$ denote the categories of Koszul-like modules and modules with linear presentations (see [1]–[3], etc.) respectively, and $A$ is a Koszul-like algebra. We construct new Koszul-like algebras from the known ones by the “one-point extension”. Some criteria for a graded algebra to be Koszul-like are provided. Finally, we construct many classical Koszul objects from the given Koszul-like objects.

Keywords: Koszul algebra, Koszul-like algebra/module, module with linear presentations, one-point extension, Yoneda algebra.

DOI: https://doi.org/10.4213/mzm10166

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English version:
Mathematical Notes, 2013, 93:3, 431–450

Bibliographic databases:

UDC: 512.7
Received: 12.10.2009
Revised: 20.07.2011

Citation: Lü Jia-Feng, “Koszul-Like Algebras and Modules”, Mat. Zametki, 93:3 (2013), 413–435; Math. Notes, 93:3 (2013), 431–450

Citation in format AMSBIB
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