Related papers: Deformation quantization modules II. Hochschild cl…
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 present a deformation theory associated to the higher Hochschild cohomology $H_{S^2}^*(A,A)$. We also study a $G$-algebra structure associated to this deformation theory.
We study the ``twisted" Poincar\'e duality of smooth Poisson manifolds, and show that, if the modular vector field is diagonalizable, then there is a mixed complex associated to the Poisson complex, which, combining with the twisted…
An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in…
If A is a bialgebra over a field k and M, N are either left-right Yetter-Drinfel'd modules or left-right Hopf modules over A, we construct deformation cohomologies H^*(M,N) as total cohomologies of certain double complexes Y(M,N) and…
Motivated by deformation quantization we consider $^*$-algebras over ordered rings and their deformations: we investigate formal associative deformations compatible with the $^*$-involution and discuss a cohomological description in terms…
The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…
Let \pi: Y -> X be a crepant projective resolution of an affine symplectic variety X with a good C^*-action. We interpret the second cohomology H^2(Y, C) in two ways. First, H^2(Y, C) is the Picard group of Y tensorised with C. By the ample…
We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…
We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for the full modular group. In many cases these modules are free or decompose at least into well-understood pieces. We…
We study the twisted Hochschild homology of quantum flag manifolds, the twist being the modular automorphism of the Haar state. We prove that every quantum flag manifold admits a non-trivial class in degree two, with an explicit…
Given a graded $E_1$-module over an $E_2$-algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution, whose graded connectivity yields homological stability for…
We explain how deformation theories of geometric objects such as complex structures, Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poisson algebras. We use homological perturbation theory to…
Bihom-associative algebras have been recently introduced in the study of group hom-categories. In this paper, we introduce a Hochschild type cohomology for bihom-associative algebras with suitable coefficients. The underlying cochain…
The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…
We first want to consider the formal deformation of a fibered manifold $P \rightarrow M$ as a (bi-)module or subalgebra, where $M$ has a given differential star product. Consequently we want to find obstructions for the existence of a…
We put in a general framework the situations in which a Riemannian manifold admits a family of compatible complex structures, including hyperkahler metrics and the Spin-rotations of arxiv:1302.2846. We determine the (polystable) holomorphic…
Deformations of a Courant Algebroid E and its Dirac subbundle A have been widely considered under the assumption that the pseudo-Euclidean metric is fixed. In this paper, we attack the same problem in a setting that allows the…
We define a notion of categorical first order deformations for (enhanced) triangulated categories. For a category $\mathcal{T}$, we show that there is a bijection between $\operatorname{HH}^2(\mathcal{T})$ and the set of categorical…
We discuss a general construction of a deformation of a smash product algebra coming from an action of a particular Hopf algebra. This Hopf algebra is generated by skew-primitive and group-like elements, and depends on a complex parameter.…