Related papers: Holomorphic Koszul-Brylinski Homology

We provide a complete list of two- and three-component Poisson structures of hydrodynamic type with degenerate metric, and study their homogeneous deformations. In the non-degenerate case any such deformation is trivial, that is, can be…

Let X be a surface with an isolated singularity at the origin, given by the equation Q(x,y,z)=0, where Q is a weighted-homogeneous polynomial. In particular, this includes the Kleinian surfaces X = C^2/G for G < SL(2,C) finite. Let Y be the…

We prove a duality for factorization homology which generalizes both usual Poincar\'e duality for manifolds and Koszul duality for $\mathcal{E}_n$-algebras. The duality has application to the Hochschild homology of associative algebras and…

We formulate the (co)bar construction theory of dg $K$-(co)rings and the calculus theory of the Hochschild homology and cohomology of dg $K$-rings. As applications, we compare the Hochschild (co)homologies of a complete typical dg $K$-ring…

We show that there exists a natural non-degenerate pairing of the homomorphism space between two neighbor standard modules over a quasi-hereditary algebra with the first extension space between the corresponding costandard modules and vise…

We study the tangential Poisson cohomology (TP-cohomology) of regular Poisson manifolds, first defined by Lichnerowicz using contravariant tensor fields. We show that for a regular Poisson manifold M, the TP-cohomology coincides with the…

We study the Poisson (co)homology of the algebra of truncated polynomials in two variables viewed as the semi-classical limit of a quantum complete intersection studied by Bergh and Erdmann. We show in particular that the Poisson cohomology…

We describe the differential graded Lie algebras governing Poisson deformations of a holomorphic Poisson manifold and coisotropic embedded deformations of a coisotropic holomorphic submanifold. In both cases, under some mild additional…

We introduce for any Poisson algebra a bicomplex of free Poisson modules, and use it to show that the Poisson cohomology theory introduced in the paper "[M. Flato, M. Gerstenhaber and A. A. Voronov, Cohomology and Deformation of Leibniz…

We show that Deformation Quantization of quadratic Poisson structures preserves the $A_\infty$-Morita equivalence of a given pair of Koszul dual $A_\infty$-algebras.

A version of the twisted Poincar\'{e} duality is proved between the Poisson homology and cohomology of a polynomial Poisson algebra with values in an arbitrary Poisson module. The duality is achieved by twisting the Poisson module structure…

The Hopf dual $H^\circ$ of any Poisson Hopf algebra $H$ is proved to be a co-Poisson Hopf algebra provided $H$ is noetherian. Without noetherian assumption, it is not true in general. There is no nontrivial Poisson Hopf structure on the…

We study different algebraic and geometric properties of Heisenberg invariant Poisson polynomial quadratic algebras. We show that these algebras are unimodular. The elliptic Sklyanin-Odesskii-Feigin Poisson algebras $q_{n,k}(\mathcal E)$…

We construct a self-dual complete resolution of a module defined by a pair of embedded complete intersection ideals in a local ring. Our construction is based on a gluing construction of Herzog and Martsinkovsky and exploits the structure…

For a perfect field $k$ of characteristic $p>0$ and a smooth and proper formal scheme $\mathscr{X}$ over the ring of integers of a finite and totally ramified extension $K$ of $W(k)[1/p]$, we propose a cohomological construction of the…

In recent years methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this note it is shown that the latter method is actually…

Factorization homology theories of topological manifolds, after Beilinson, Drinfeld and Lurie, are homology-type theories for topological $n$-manifolds whose coefficient systems are $n$-disk algebras or $n$-disk stacks. In this work we…

Felder and Kazhdan conjecture that the local cohomology in the classical Batalin-Vilkovisky formalism vanishes in sufficiently negative degrees. This hypothesis is violated by the $N=1$ spinning particle. By Barnich-Grigoriev, this…

This paper studies differential graded modules and representations up to homotopy of Lie $n$-algebroids, for general $n\in\mathbb{N}$. The adjoint and coadjoint modules are described, and the corresponding split versions of the adjoint and…

We solve a functional version of the problem of twist quantization of a coboundary Lie bialgebra (g,r,Z). We derive from this the following results: (a) the formal Poisson manifolds g^* and G^* are isomorphic; (b) we construct a subalgebra…