19 research outputs found
Cohomologie de Chevalley des graphes ascendants
The space of all tensor fields on ,
equipped with the Schouten bracket is a Lie algebra. The subspace of ascending
tensors is a Lie subalgebra of . In this paper, we
compute the cohomology of the adjoint representations of this algebra (in
itself and ), when we restrict ourselves to cochains
defined by aerial Kontsevitch's graphs like in our previous work (Pacific J of
Math, vol 229, no 2, (2007) 257-292). As in the vectorial graphs case, the
cohomology is freely generated by all the products of odd wheels
Les (a,b)-algèbres à homotopie près
We study in this article the concepts of algebra up to homotopy for a structure defined by two operations \pt and . Having determined the structure of algebras and algebras, we generalize this construction and we define a structure of -algebra up to homotopy. Given a structure of commutative and differential graded Lie algebra for two shifts degree given by and , we will give an explicit construction of the associate algebra up to homotop
Algèbres et cogèbres de Gerstenhaber et cohomologie de Chevalley-Harrison
The fundamental example of Gerstenhaber algebra is the space of polyvector fields on , equipped with the wedge product and the Schouten bracket. In this paper, we explicitely describe what is the enveloping algebra of a Gerstenhaber algebra . This structure gives us a definition of the Chevalley-Harrison cohomology operator for . We finally show the nontriviality of a Chevalley-Harrison cohomology group for a natural Gerstenhaber subalgebra in