Related papers: Poisson-Lie Odd Bracket on Grassmann Algebra

Quadratic Poisson brackets on associative algebras are studied. Such a bracket compatible with the multiplication is related to a differentiation in tensor square of the underlying algebra. Jacobi identity means that this differentiation…

The paper is withdrawn.

All possible graded Poisson-Lie structures on the external algebra of $SL(2)$ are described. We prove that differential Poisson-Lie structures prolonging the Sklyanin brackets do not exist on $SL(2)$. There are two and only two graded…

This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.

This paper has been withdrawn

It is shown that two definitions for an exterior differential in superspace, giving the same exterior calculus, yet lead to different results when applied to the Poisson bracket. A prescription for the transition with the help of these…

The paper has been withdrawn.

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…

This paper has been withdrawn by the corresponding author because the newest version is now published in Journal of Discrete Algorithms.

Poisson algebras have become an essential topic in mathematics with a rich structure and wide applicability. Despite numerous resources available on Poisson structures, the algebraic side of the story remains relatively less explored. This…

This paper has been withdrawn because it is a duplicate of [math/0609208].

This paper has been withdrawn by the author, due to possible counter-examples.

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…

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…

A duality invariant action for (1,1) supersymmetric extension of Poisson-Lie dualizable $\sigma$-models is constructed.

The paper was withdrawn due to a gap in the proof of Lemma 3.

There have been gaps found in the proofs. The paper is withdrawn until further notice.

Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on n-dimensional space taking values in a Grassmann algebra with m generating elements are described up to an equivalence…

This paper has been withdrawn since it is identical to the paper math.QA/0601267. It was posted by mistake.

This paper has been withdrawn by authors for significant modification.