Related papers: Deformation quantisation for (-1)-shifted symplect…
A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the $h$-deformed…
We study the deformation complex of the dg wheeled properad of $\mathbb{Z}$-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application we show that the…
We investigate formal deformations of certain classes of nonassociative algebras including classes of K[{\Sigma}3]-associative algebras, Lie-admissible algebras and anti-associative algebras. In a process which is similar to Poisson algebra…
We explicitly describe cohomology of the sheaf of differential forms with poles along a semiample divisor on a complete simplicial toric variety. As an application, we obtain a new vanishing theorem which is an analogue of the…
We generalize the construction of a moduli space of semistable pairs parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to any sheaf with fixed Hilbert polynomial under a notion of stability to the case of projective…
We generalize a vanishing theorem for the cohomology of symmetric powers of the cotangent bundle of subvarieties of projective space due to Schneider. From this we deduce new vanishing results for Green-Griffiths jet differential bundles,…
The purpose of this paper is to apply deformation quantization to the study of the coadjoint orbit method in the case of real reductive groups. We first prove some general results on the existence of equivariant deformation quantization of…
The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the…
I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with…
Let $M$ be a smooth manifold equipped with a conformal structure, $E[w]$ the space of densities with the the conformal weight $w$ and $D_{w,w+\de}$ the space of differential operators from $E[w]$ to $E[w+\delta]$. Conformal quantization $Q$…
Cohomological Yang-Mills theory is formulated on a noncommutative differentiable four manifold through the $\theta$-deformation of its corresponding BRST algebra. The resulting noncommutative field theory is a natural setting to define the…
We suppose that the ground-state eigenvalue E = F(v) of the Schroedinger Hamiltonian H = -\Delta + vf(x) in one dimension is known for all values of the coupling v > 0. The potential shape f(x) is assumed to be symmetric, bounded below, and…
We investigate the Poisson geometry of the Marsden-Weinstein reductions of the moment map associated to the cotangent bundle of the space of representations of a quiver. We show that the stratification by representation type equals the…
A factorization formula for certain automorphisms of a Poisson algebra associated to a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing…
A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. The Hilbert space of states is realized via the Bott-Borel-Weil theorem in…
Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd. We exhibit in…
We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact…
The quantum double construction of a $q$-deformed boson algebra possessing a Hopf algebra structure is carried out explicitly. The $R$-matrix thus obtained is compared with the existing literature.
Kashiwara, Polesello, Schapira and D'Agnolo defined canonical deformation quantizations of a holomorphic symplectic manifold and a holomorphic Lagrangian submanifold equipped with an orientation data. The goal of this paper is to use…
For a smooth finite cyclic covering over a projective space of dimension greater than one, we show that the group of automorphisms acts faithfully on the cohomology except for a few cases. In characteristic zero, we study the equivariant…