no. 12
Algebra
Graded algebras and multilinear forms
[Algèbres graduées et formes multilinéaires]

Présenté par : Alain Connes

Dubois-Violette, Michel1
1 Laboratoire de physique théorique, UMR 8627, université Paris XI, bâtiment 210, 91405 Orsay cedex, France
Comptes Rendus. Mathématique, Tome 341 (2005) no. 12, pp. 719-724.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.10.017
Dubois-Violette, Michel 1

1 Laboratoire de physique théorique, UMR 8627, université Paris XI, bâtiment 210, 91405 Orsay cedex, France 
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Dubois-Violette, Michel. Graded algebras and multilinear forms. Comptes Rendus. Mathématique, Tome 341 (2005) no. 12, pp. 719-724. doi : 10.1016/j.crma.2005.10.017. http://www.numdam.org/articles/10.1016/j.crma.2005.10.017/

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