Related papers: Holomorphic Koszul-Brylinski Homology

In this paper, we compute the Poisson (co)homology of a polynomial Poisson structure given by two Casimir polynomial functions which define a complete intersection with an isolated singularity.

In this paper, we study restricted Poisson algebras in characteristic 2 and their relationship with restricted Lie-Rinehart algebras, for which we develop a cohomology theory and investigate abelian extensions. We also construct a full…

In this paper, we develop holomorphic Jacobi structures. Holomorphic Jacobi manifolds are in one-to-one correspondence with certain homogeneous holomorphic Poisson manifolds. Furthermore, holomorphic Poisson manifolds can be looked at as…

Recantly, William Crawley-Boevey proposed the definition of a Poisson structure on a noncommutative algebra $A$ based on the Kontsevich principle. His idea was to find the {\it weakest} possible structure on $A$ that induces standard…

We prove that the factorization homologies of a scheme with coefficients in truncated polynomial algebras compute the cohomologies of its generalized configuration spaces. Using Koszul duality between commutative algebras and Lie algebras,…

We construct an explicit isomorphism between (truncations of) quiver Hecke algebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-Samelson bimodules. As a corollary, we deduce that the decomposition numbers of these…

We prove that Hochschild cohomology with coefficients in $A^*=\Hom_k(A,k)$ under conditions on the algebra structure of $A^*$ is a Batalin-Vilkovisky algebra. We also show that for symmetric and Frobenius algebras, this recovers the known…

This paper is the continuation of arXiv:0802.1245. We construct the Hochschild class for coherent modules over a deformation quantization algebroid on a complex Poisson manifold. We also define the convolution of Hochschild homologies, and…

A well-known and old result of Hazewinkel and Koszul states that the cohomology of a finite-dimensional Lie algebra is isomorphic, up to a suitable shift, to its twisted homology, a Lie-theoretical version of Poincare duality. This paper…

Applying recent results by Lowen-Van den Bergh we show that Hochschild cohomology is preserved under Koszul-Moore duality as a Gerstenhaber algebra. More precisely, the corresponding Hochschild complexes are linked by a quasi-isomorphism of…

To each polynomial $\v\in\F[x,y,z]$ is associated a Poisson structure on $\F^3$, a surface and a Poisson structure on this surface. When $\v$ is weight homogeneous with an isolated singularity, we determine the Poisson cohomology and…

For a system of non-homogeneous polynomials it was constructed explicit complex morphism of a dual complex to the Koszul complex into the Koszul complex. If the ideal of these polynomials is 0-dimensional, then this mapping is a homotopic…

This paper is a sequel to [Caine A., Pickrell D., arXiv:0710.4484], where we studied the Hamiltonian systems which arise from the Evens-Lu construction of homogeneous Poisson structures on both compact and noncompact type symmetric spaces.…

We develop the Hochschild analogue of the coniveau spectral sequence and the Gersten complex. Since Hochschild homology does not have devissage or A^1-invariance, this is a little different from the K-theory story. In fact, the rows of our…

Let V be a holomorphic bundle over a complex manifold M, and s be a holomorphic section of V. We study different types of cohomology associated to the Koszul complex induced by s. When M is complete, these cohomologies are isomorphic to…

We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples include the shifted de Rham complex of a Poisson manifold and the…

We prove that the (homotopy) hypercommutative algebra structure on the de Rham cohomology of a Poisson or Jacobi manifold defined by several authors is (homotopically) trivial, i.e. it reduces to the underlying (homotopy) commutative…

We geometrize the constructions of twisted Poisson modules introduced by Luo-Wang-Wu, and Poisson chain complexes with coefficients in Poisson modules defined in the algebraic setting to the geometric setting of Poisson manifolds. We then…

In this paper, we study invariant Poisson structures on homogeneous manifolds, which serve as a natural generalization of homogeneous symplectic manifolds previously explored in the literature. Our work begins by providing an algebraic…

We show (modulo a parity condition) that, a generalized complex brane in a generalized complex manifold is locally equivalent to a holomorphic coisotropic submanifold of a holomorphic Poisson structure, with higher-rank branes corresponding…