Related papers: Nearly associative deformation quantization
We introduce a new type of noncommutative Poisson structure on associative algebras. It induces Poisson structures on the moduli spaces classifying semisimple modules. Path algebras of doubled quivers and preprojective algebras have…
In this paper we investigate classifications of all (transposed) Poisson algebras of the associated associative null-filiform algebra
It is known that, for the algebra of functions on a Kleinian singularity, the parameter space of deformations and the parameter space of quantizations coincide. We prove that, for a Kleinian singularity of type $\mathbf{A}$ or $\mathbf{D}$,…
We define admissible quasi-Hopf quantized universal enveloping (QHQUE) algebras by h-adic valuation conditions. We show that any QHQUE algebra is twist-equivalent to an admissible one. We prove a related statement: any associator is…
The aim of the paper is twofold. First, we introduce analogs of (partial) derivatives on certain Noncommutative algebras, including some enveloping algebras and their "braided counterparts", namely, the so-called modified Reflection…
Poisson superalgebras are known as a $\mathbb{Z}_2$-graded vector space with two operations, an associative supercommutative multiplication and a super bracket tied up by the super Leibniz relation. We show that we can consider a single…
In this paper we prove the existence of isomorphisms between certain non-commutative algebras that are interesting from representation theoretic perspective and arise as quantizations of certain Poisson algebras. We show that quantizations…
Finding identities in nonassociative algebras plays an important role in the study of properties of these algebras. In this paper, we present some identities in alternative algebras and in algebras obtained by the Cayley-Dickson process.…
We consider Poisson superalgebras with constant nondegenerate bracket realized on the smooth Grassmann-valued functions with compact supports in R^{2n}. The deformations with even and odd deformation parameters of these superalgebras are…
After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologies on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and…
We study $\mathbb Z_2$-graded Poisson structures defined on $\mathbb Z_2$-graded commutative polynomial algebras. In small dimensional cases, we exhibit classifications of such Poisson structures, obtain the associated Poisson $\mathbb…
A simple iterative procedure is suggested for the deformation quantization of (irregular) Poisson brackets associated to the classical Yang-Baxter equation. The construction is shown to admit a pure algebraic reformulation giving the…
In this paper we prove that any Poisson structure on a sheaf of Lie algebroids admits a weak deformation quantization, and give a sufficient condition for such a Poisson structure to admit an actual deformation quantization. We also answer…
We compare three different ways of checking the Jacobi identity for weakly nonlocal Poisson brackets using the theory of distributions, of pseudodifferential operators and of Poisson vertex algebras, respectively. We show that the three…
We express the difference between Poisson bracket and deformed bracket for Kontsevich deformation quantization on any Poisson manifold by means of second derivative of the formality quasi-isomorphism. The counterpart on star products of the…
We define noncommutative deformations $W_q^s(G)$ of algebras of functions on certain (finite coverings of) transversal slices to the set of conjugacy classes in an algebraic group $G$ which play the role of Slodowy slices in algebraic group…
We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category…
In this paper we construct a deformation quantization of the algebra of polynomials of an arbitrary (regular and non regular) coadjoint orbit of a compact semisimple Lie group. The deformed algebra is given as a quotient of the enveloping…
Noncommutative or `quantum' differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics) but also differential forms, bundles and…
Quantum deformations of the structure constants for a class of associative noncommutative algebras are studied. It is shown that these deformations are governed by the quantum central systems which has a geometrical meaning of vanishing…