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| HAL: hal-00547749, version 2 |
| arXiv: 1012.3885 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2010-12-17) | v2 (2011-10-11) |
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| Alternated Hochschild Cohomology |
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| Pierre B.A. Lecomte 1Valentin Ovsienko 2 |
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| (2010-12-17) |
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| In this paper we construct a graded Lie algebra on the space of cochains on a $\mathbbZ_2$-graded vector space that are skew-symmetric in the odd variables. 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''. 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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| Subject | : | Mathematics/Rings and Algebras Mathematics/Quantum Algebra |
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| Hochschild cohomology – graded Lie algebra – Lie antialgebra. |
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| Attached file list to this document: | ||||||||||
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| hal-00547749, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00547749 | |
| oai:hal.archives-ouvertes.fr:hal-00547749 | |
| From: Valentin Ovsienko | |
| Submitted on: Tuesday, 11 October 2011 06:19:58 | |
| Updated on: Tuesday, 11 October 2011 14:30:28 | |
