Related papers: Categorical Perspective on Quantization of Poisson…

A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position. Special values of the parameters are characterized by the…

There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]={f,g} for any two functions f and g. We notice that this non-commutative differential algebra has a geometrical…

This paper provides a short introduction to the notion of regular category and its use in categorical algebra. We first prove some of its basic properties, and consider some fundamental algebraic examples. We then analyse the algebraic…

We introduce the \emph{universal algebra} of two Poisson algebras $P$ and $Q$ as a commutative algebra $A:={\mathcal P} (P, \, Q )$ satisfying a certain universal property. The universal algebra is shown to exist for any finite dimensional…

Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides…

The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.

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…

Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras is initiated. Connections are established that relate…

Based on the monoid classifier, we give an alternative axiomatization of Freyd's paracategories, which can be interpreted in any bicategory of partial maps. Assuming furthermore a free-monoid monad T in our ambient category, and…

We introduce the notion of Gamma-Lie bialgebra, where Gamma is a group. These objects give rise to cocommutative co-Poisson algebras, for which we construct quantization functors. This enlarges the class of co-Poisson algebras for which a…

In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple…

It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra. We also generalize the Hamiltonian Lie algebra using…

Motivated by the universal obstruction to the deformation quantization of Poisson structures in infinite dimensions we introduce the notion of quantizable odd Lie bialgebra. The main result of the paper is a construction of a highly…

This note is an overview of the Poisson sigma model (PSM) and its applications in deformation quantization. Reduction of coisotropic and pre-Poisson submanifolds, their appearance as branes of the PSM, quantization in terms of L-infinity…

We construct quadratic finite-dimensional Poisson algebras and their quantum versions related to rank N and degree one vector bundles over elliptic curves with n marked points. The algebras are parameterized by the moduli of curves. For N=2…

We introduce the notion of a majority category --- the categorical counterpart of varieties of universal algebras admitting a majority term. This notion can be thought to capture properties of the category of lattices, in a way that…

The V-algebras are the non-local matrix generalization of the well-known W-algebras. Their classical realizations are given by the second Poisson brackets associated with the matrix pseudodifferential operators. In this paper, by using the…

In a recent paper, motivated by the study of central extensions of associative algebras, G. Janelidze introduces the notion of weakly action representable category. In this paper, we show that the category of Leibniz algebras is weakly…

We re-formulate Bezrukavnikov-Kaledin's definition of a restricted Poisson algebra, provide some natural and interesting examples, and discuss connections with other research topics.

The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental…