Geodesic
Koszul-Like Algebras and Modules
Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 413-435

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Mots-clés : Koszul algebra, Koszul-like algebra/module
Keywords: module with linear presentations, one-point extension, Yoneda algebra. 
@article{MZM_2013_93_3_a9,
     author = {L\"u Jia-Feng},
     title = {Koszul-Like {Algebras} and {Modules}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {413--435},
     publisher = {mathdoc},
     volume = {93},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a9/}
}
TY  - JOUR
AU  - Lü Jia-Feng
TI  - Koszul-Like Algebras and Modules
JO  - Matematičeskie zametki
PY  - 2013
SP  - 413
EP  - 435
VL  - 93
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a9/
LA  - ru
ID  - MZM_2013_93_3_a9
ER  - 
%0 Journal Article
%A Lü Jia-Feng
%T Koszul-Like Algebras and Modules
%J Matematičeskie zametki
%D 2013
%P 413-435
%V 93
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a9/
%G ru
%F MZM_2013_93_3_a9
Lü Jia-Feng. Koszul-Like Algebras and Modules. Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 413-435. http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a9/