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| HAL : hal-00547749, version 1 |
| arXiv : 1012.3885 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (17-12-2010) | v2 (11-10-2011) |
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| Alternated Hochschild Cohomology |
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| Pierre B.A. Lecomte 1Valentin Ovsienko 2 |
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| (17/12/2010) |
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| In this paper we construct a graded Lie algebra on the space of cochains on a $\bbZ_2$-graded vector space $V=V_0\oplus{}V_1$ that are skew-symmetric on the subspace $V_1$. The Lie bracket is obtained from the classical Gerstenhaber bracket by (partial) skew-symmetrization; the coboundary operator is a skew-symmetrized version of the Hochschild differential. We show that an order-one element $m$ satisfying the zero-square condition $[m,m]=0$ defines an algebraic structure called ``Lie antialgebra'' in \cite{Ovs}. The cohomology (and deformation) theory of these algebras is then defined. We present two examples of non-trivial cohomology classes which are similar to the celebrated Gelfand-Fuchs and Godbillon-Vey classes. |
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| 1 : | Geothalg |
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University of Liège |
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| 2 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| Domaine | : | Mathématiques/Anneaux et algèbres Mathématiques/Algèbres quantiques |
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| Hochschild cohomology – graded Lie algebra – Lie antialgebra. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00547749, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00547749 | |
| oai:hal.archives-ouvertes.fr:hal-00547749 | |
| Contributeur : Valentin Ovsienko | |
| Soumis le : Vendredi 17 Décembre 2010, 11:31:33 | |
| Dernière modification le : Vendredi 17 Décembre 2010, 15:18:51 | |
