Poisson (co)homology of truncated polynomial algebras in two variables

Stéphane Launois; Lionel Richard

doi:10.1016/j.crma.2008.12.005

Algebra/Homological Algebra

Poisson (co)homology of truncated polynomial algebras in two variables

Presented by: Michèle Vergne

Stéphane Launois ¹; Lionel Richard ²

¹ Institute of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7NF, UK
² School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK

Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 133-138.

Abstract
Résumé

We study the Poisson (co)homology of the algebra of truncated polynomials in two variables viewed as the semi-classical limit of a quantum complete intersection studied by Bergh and Erdmann. We show in particular that the Poisson cohomology ring of such a Poisson algebra is isomorphic to the Hochschild cohomology ring of the corresponding quantum complete intersection.

Nous étudions la cohomologie de Poisson d'une algèbre de polynômes tronqués en deux indéterminées vue comme la limite semi-classique des intersections complètes quantiques étudiées par Bergh et Erdmann. Nous montrons en particulier que l'anneau de cohomologie de Poisson de cette algèbre de Poisson est isomorphe à l'anneau de cohomologie de Hochschild de l'intersection complète quantique associée.

Received: 2008-06-06
Accepted: 2008-12-10
Published online: 2009-01-29

DOI: 10.1016/j.crma.2008.12.005

Author's affiliations:

Stéphane Launois ¹; Lionel Richard ²

¹ Institute of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7NF, UK
² School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK

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     author = {St\'ephane Launois and Lionel Richard},
     title = {Poisson (co)homology of truncated polynomial algebras in two variables},
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     pages = {133--138},
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     doi = {10.1016/j.crma.2008.12.005},
     language = {en},
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Stéphane Launois; Lionel Richard. Poisson (co)homology of truncated polynomial algebras in two variables. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 133-138. doi : 10.1016/j.crma.2008.12.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.12.005/

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