15 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
Hom-Lie quadratic and Pinczon Algebras
International audienc
AlgÚbres pré-Gerstenhaber à homotopie prÚs
This paper is concerned by the concept of algebra up to homotopy for a structure defined by two operations and . An important example of such a structure is the Gerstenhaber algebra (commutatitve and Lie). The notion of Gerstenhaber algebra up to homotopy ( algebra) is known. Here, we give a definition of pre-Gerstenhaber algebra (pre-commutative and pre-Lie) allowing the construction of algebra. Given a structure of pre-commutative (Zinbiel) and pre-Lie algebra and working over the corresponding dual operads, we will give an explicit construction of the associated pre-Gerstenhaber algebra up to homotopy, this is a bicogebra (Leibniz and permutative) equipped with a codifferential which is a coderivation for the two coproducts
AlgÚbre Pré-Gerstenhaber à homotopie prÚs
International audienceRĂ©sumĂ©. On Ă©tudie le concept d'algĂšbre Ă homotopie prĂšs pour une structure dĂ©finie par deux opĂ©rations . et [ , ]. Un exemple important d'une telle structure est celui d'algĂšbre de Gerstenhaber (avec une structure commutative de degrĂ© 0 et une structure de Lie de degrĂ© â1). La notion d'algĂšbre de Gerstenhaber Ă homotopie prĂšs (Gâ algĂšbre) est connue : c'est une bicogĂšbre codiffĂ©rentielle.Ici nous proposons une dĂ©finition d'algĂšbre prĂ©-Gerstenhaber (prĂ©-commutative et prĂ©-Lie) permettant la construction similaire d'une preGâ algĂšbre.Partant d'une structure prĂ©-commutative (Zinbiel) et prĂ©-Lie, on utilise les opĂ©rades duales correspondantes, qui sont de Koszul. Nous donnons la construction explicite de l'algĂšbre Ă homotopie prĂšs associĂ©e. Celle-ci est une bicogĂšbre (Leibniz et permutative), munie d'une codiffĂ©rentielle qui est une codĂ©rivation des deux coproduits.Abstract. This paper is concerned by the concept of algebra up to homotopy for a structure defined by two operations . and [ , ]. An important example of such a structure is the Gerstenhaber algebra (i.e. commutatitve structure with degree 0 and Lie structure with degree â1). The notion of Gerstenhaber algebra up to homotopy (Gâ algebra) is known: it is a codifferential bicogebra.Here, we give a definition of pre-Gerstenhaber algebra (pre-commutative and pre-Lie) allowing a similar construction for a preGâ algebra.Given a structure of pre-commutative (Zinbiel) and pre-Lie algebra and working over the corresponding Koszul dual operads, we will give an explicit construction of the associated pre-Gerstenhaber algebra up to homotopy: it is a bicogebra (Leibniz and permutative) equipped with a codifferential which is a coderivation for the two coproducts
AlgĂšbres et cogĂšbres 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