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Comptes Rendus Mathématique
Volume 341, n° 12
pages 719-724 (décembre 2005)
Doi : 10.1016/j.crma.2005.10.017
Received : 24 August 2005 ;  accepted : 11 October 2005
Graded algebras and multilinear forms
Algèbres graduées et formes multilinéaires
 

Michel Dubois-Violette
Laboratoire de physique théorique, UMR 8627, université Paris XI, bâtiment 210, 91405 Orsay cedex, France 

Abstract

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. To cite this article: M. Dubois-Violette, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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Résumé

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. Pour citer cet article : M. Dubois-Violette, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.


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