Related papers: Transposed Poisson structures

This paper is the third in a series of papers, the aim of which is to construct algebraic geometry over metabelian Lie algebras.

Motivated by a problem in graph theory, this article introduces an algebra called the balanced algebra. This algebra is defined by generators and relations, and the main goal is to find a minimal set of relations for it.

In this paper, we consider Hamiltonian structures of hydrodynamic type and some of their generalizations. In particular, we discuss the questions concerning the structure and special forms of the corresponding Poisson brackets and the…

This paper is a short survey about some properties of algebras ob- tained by the Cayley-Dickson process and some of their applications.

A brief survey of some aspects of noetherian Hopf algebras is given, concentrating on structure, homology, and classification, and accompanied by a panoply of open problems.

Let $X$ be a finite connected poset, $K$ a field of characteristic zero and $I(X,K)$ the incidence algebra of $X$ over $K$ seen as a Lie algebra under the commutator product. In the first part of the paper we show that any…

After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such…

The purpose of this paper is to construct topology on vague soft sets. The concept of vague soft topology is introduced and its basic properties are given.

The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…

Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables…

We are interested in Poisson structures transverse to nilpotent adjoint orbits in a complex semi-simple Lie algebra, and we study their polynomial nature, introduced by R.Cushman and M.Roberts. Furthermore, in the case of sl(n), we…

This document aims to be a self-contained, mathematically precise overview of transformer architectures and algorithms (*not* results). It covers what transformers are, how they are trained, what they are used for, their key architectural…

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…

We define algebras of admissible functions associated to twisted Dirac structures, and we show that they are Poisson algebras. We study the standard cases associated to Dirac structures defined by graphs of non-degenerate 2-forms.

We investigate the geometric, algebraic and homologic structures related with Poisson structure on a smooth manifold. Introduce a noncommutative foundations of these structures for a Poisson algebra. Introduce and investigate noncommutative…

We describe a new algebraic structure of "deformed chiral algebra" motivated by the study of the deformed W-algebras. We use it to gain some insights into the deformed Virasoro algebra.

We introduce and study suitable Poisson structures for four dimensional maps derived as lifts and specific periodic reductions of integrable lattice equations. These maps are Poisson with respect to these structures and the corresponding…

We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.

We prove an equivariant version of the local splitting theorem for tame Poisson structures and Poisson actions of compact Lie groups. As a consequence, we obtain an equivariant linearization result for Poisson structures whose transverse…

We give a definition of coisotropic morphisms of shifted Poisson (i.e. $P_n$) algebras which is a derived version of the classical notion of coisotropic submanifolds. Using this we prove that an intersection of coisotropic morphisms of…