Graded algebras and multilinear forms

Michel Dubois-Violette

doi:10.1016/j.crma.2005.10.017

Algebra

Graded algebras and multilinear forms

Presented by: Alain Connes

Michel Dubois-Violette ¹

¹ Laboratoire de physique théorique, UMR 8627, université Paris XI, bâtiment 210, 91405 Orsay cedex, France

Comptes Rendus. Mathématique, Volume 341 (2005) no. 12, pp. 719-724.

Abstract
Résumé

We give a description of the connected graded algebras which are finitely generated and presented of global dimension 2 or 3 and which are Gorenstein. These algebras are constructed from multilinear forms. We generalize the construction by associating homogeneous algebras to multilinear forms. The homogeneous algebras which are Koszul of finite global dimension and which are Gorenstein of this type.

Nous donnons une description des algèbres graduées connexes de présentation finie et de dimension globale 2 ou 3 qui sont Gorenstein. Ces algèbres sont construites à partir de formes multilinéaires. Cette construction est généralisée en associant des algèbres homogènes aux formes multilinéaires. Sont de ce type les algèbres homogènes Koszul–Gorenstein de dimension globale finie.

Received: 2005-08-24
Accepted: 2005-10-11
Published online: 2005-11-18

DOI: 10.1016/j.crma.2005.10.017

Author's affiliations:

Michel Dubois-Violette ¹

¹ Laboratoire de physique théorique, UMR 8627, université Paris XI, bâtiment 210, 91405 Orsay cedex, France

@article{CRMATH_2005__341_12_719_0,
     author = {Michel Dubois-Violette},
     title = {Graded algebras and multilinear forms},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {719--724},
     publisher = {Elsevier},
     volume = {341},
     number = {12},
     year = {2005},
     doi = {10.1016/j.crma.2005.10.017},
     language = {en},
}

TY  - JOUR
AU  - Michel Dubois-Violette
TI  - Graded algebras and multilinear forms
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 719
EP  - 724
VL  - 341
IS  - 12
PB  - Elsevier
DO  - 10.1016/j.crma.2005.10.017
LA  - en
ID  - CRMATH_2005__341_12_719_0
ER  -

%0 Journal Article
%A Michel Dubois-Violette
%T Graded algebras and multilinear forms
%J Comptes Rendus. Mathématique
%D 2005
%P 719-724
%V 341
%N 12
%I Elsevier
%R 10.1016/j.crma.2005.10.017
%G en
%F CRMATH_2005__341_12_719_0

Michel Dubois-Violette. Graded algebras and multilinear forms. Comptes Rendus. Mathématique, Volume 341 (2005) no. 12, pp. 719-724. doi : 10.1016/j.crma.2005.10.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.10.017/

References
Cited by

[1] M. Artin; W.F. Schelter Graded algebras of global dimension 3, Adv. Math., Volume 66 (1987), pp. 171-216

[2] M. Artin; J. Tate; M. Van den Bergh Modules over regular algebras of dimension 3, Invent. Math., Volume 106 (1991), pp. 335-388

[3] R. Berger Koszulity for nonquadratic algebras, J. Algebra, Volume 239 (2001), pp. 705-734

[4] R. Berger; M. Dubois-Violette; M. Wambst Homogeneous algebras, J. Algebra, Volume 261 (2003), pp. 172-185

[5] R. Berger; N. Marconnet Koszul and Gorenstein properties for homogeneous algebras | arXiv

[6] A. Connes; M. Dubois-Violette Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples, Comm. Math. Phys., Volume 230 (2002), pp. 539-579

[7] A. Connes; M. Dubois-Violette Yang–Mills algebra, Lett. Math. Phys., Volume 61 (2002), pp. 149-158

[8] A. Connes; M. Dubois-Violette Moduli space and structure of noncommutative 3-spheres, Lett. Math. Phys., Volume 66 (2003), pp. 91-121

[9] A. Connes; M. Dubois-Violette Yang–Mills and some related algebras | arXiv

[10] M. Dubois-Violette; G. Launer The quantum group of a non-degenerated bilinear form, Phys. Lett. B, Volume 245 (1990), pp. 175-177

[11] M. Dubois-Violette; T. Popov Homogeneous algebras, statistics and combinatorics, Lett. Math. Phys., Volume 61 (2002), pp. 159-170

[12] R.S. Irving Prime ideals of Ore extensions, J. Algebra, Volume 58 (1979), pp. 399-423

Cited by Sources:

Comments - Policy