Alternated Hochschild Cohomology

نویسندگان

  • Pierre Lecomte
  • Valentin Ovsienko
چکیده

In this paper we construct a graded Lie algebra on the space of cochains on a Z2-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” in [17]. 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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تاریخ انتشار 2011