Some properties of the extremal algebras

Shengqiang Wang; Quanshui Wu

doi:10.1016/j.crma.2014.09.028

Algebra/Homological algebra

Some properties of the extremal algebras
[Quelques propriétés des algèbres extrémales]

Présenté par : the Editorial Board

Shengqiang Wang ¹ ; Quanshui Wu ²

¹ Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
² School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 985-990.

Résumé
Abstract

En nous appuyant sur les travaux de Fløystad et Vatne, nous décrivons quelques propriétés homologiques des algèbres extrémales. Plus précisément, nous montrons que les algèbres extrémales sont intègres, nœthériennes, régulières au sens d'Auslander, de Cohen–Macaulay et de Calabi–Yau. Nous calculons également les modules cycliques de la série de Hilbert ${(1 - t)}^{- 1}$ sur ces algèbres extrémales.

The (generalized) extremal algebra [4] is Noetherian, Auslander regular and Cohen–Macaulay. A necessary and sufficient condition is given for the generalized extremal algebras being Calabi–Yau. The point modules over these algebras are described explicitly.

Reçu le : 2014-05-20
Accepté le : 2014-09-30
Publié le : 2014-10-25

DOI : 10.1016/j.crma.2014.09.028

Affiliations des auteurs :

Shengqiang Wang ¹ ; Quanshui Wu ²

¹ Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
² School of Mathematical Sciences, Fudan University, Shanghai 200433, China

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Shengqiang Wang; Quanshui Wu. Some properties of the extremal algebras. Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 985-990. doi : 10.1016/j.crma.2014.09.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.028/

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