Related papers: Poisson superbialgebras

Motivated by the study of the operator forms of the constant classical Yang-Baxter equation given by Semonov-Tian-Shansky, Kupershmidt and the others, we try to construct the rational solutions of the classical Yang-Baxter equation with…

Superimposed D-branes have matrix-valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics…

E.B. Vinberg's theory of quasi-derivations of algebras is extended to a broader framework of near-derivations. This deepens connections between Poisson geometry and Lie theory. Although basic results apply to arbitrary algebras, our…

In this paper, we develop the bialgebra theory for Lie-Yamaguti algebras. For this purpose, we exploit two types of compatibility conditions: local cocycle condition and double construction. We define the classical Yang-Baxter equation in…

In this paper, we first introduce the notion of an anti-pre-Poisson bialgebra, which is shown to be equivalent to both quadratic anti-pre-Poisson algebras and matched pairs of Poisson algebras. The study of coboundary anti-pre-Poisson…

In this paper, we introduce the notion of a left-symmetric bialgebroid as a geometric generalization of a left-symmetric bialgebra and construct a left-symmetric bialgebroid from a pseudo-Hessian manifold. We also introduce the notion of a…

We provide a quasi-Poisson version of the Drinfeld's correspondence between Poisson homogeneous spaces and Lagrangian subalgebras.

Poisson algebras are, just like Lie algebras, particular cases of Lie-Rinehart algebras. The latter were introduced by Rinehart in his seminal 1963 paper, where he also introduces the notion of an enveloping algebra and proves --- under…

A commutative Poisson subalgebra of the Poisson algebra of polynomials on the Lie algebra of n x n matrices over ${\Bbb C}$ is introduced which is the Poisson analogue of the Gelfand-Zeitlin subalgebra of the universal enveloping algebra.…

We introduce a new class of algebras called Poisson orders. This class includes the symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of unity, and enveloping algebras of restricted Lie algebras in…

It is known that the operads of perm algebras and pre-Lie algebras are the Koszul dual each other and hence there is a Lie algebra structure on the tensor product of a perm algebra and a pre-Lie algebra. Conversely, we construct a special…

Lie bialgebra structures are reviewed and investigated in terms of the double Lie algebra, of Manin- and Gau{\ss}-decompositions. The standard R-matrix in a Manin decomposition then gives rise to several Poisson structures on the…

Structures of Lie algebras, Lie coalgebras, Lie bialgebras and Lie quasibialgebras are presented as solutions of Maurer-Cartan equations on corresponding governing differential graded Lie algebras using the big bracket construction of…

Associative Yang-Baxter equation arises in different areas of algebra, e.g., when studying double quadratic Poisson brackets, non-abelian quadratic Poisson brackets, or associative algebras with cyclic 2-cocycle (anti-Frobenius algebras).…

A left-Alia algebra is a vector space together with a bilinear map satisfying symmetric Jocobi identity. Motivated by invariant theory, we first construct a class of left-Alia algebras induced by twisted derivations. Then, we introduce the…

In this paper, we define (cohomologically) 1-shifted Manin triples and 1-shifted Lie bialgebras, and study their properties. We derive many results that are parallel to those found in ordinary Lie bialgebras, including the double…

All Bianchi bialgebras have been obtained. By introducing a non-degenerate adjoint invariant inner product over these bialgebras the associated Drinfeld doubles have been constructed, then by calculating the coupling matrices for these…

Some applications of the odd Poisson bracket developed by Kharkov's theorists are represented, including the reformulation of classical Hamiltonian dynamics, the description of hydrodynamics as a Hamilton system by means of the odd bracket…

Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a…

The purpose of this paper is to study infinitesimal H-pseudobialgebra, which is an associative analogy of Lie H-pseudobialgebra. We first define the infinitesimal H-pseudobialgebra and investigate some properties of this new algebraic…