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Pré-Publication, Document De Travail Année : 2011

Alternated Hochschild Cohomology

Pierre B.A. Lecomte
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Valentin Ovsienko
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Résumé

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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Dates et versions

hal-00547749 , version 1 (17-12-2010)
hal-00547749 , version 2 (11-10-2011)

Identifiants

Citer

Pierre B.A. Lecomte, Valentin Ovsienko. Alternated Hochschild Cohomology. 2011. ⟨hal-00547749v2⟩
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