相关论文: Exterior Differentials in Superspace and Poisson B…

After a brief description of the $\mathbb{Z}$-graded differential Poisson algebra, we introduce a covariant star product for exterior differential forms and give an explicit expression for it up to second order in the deformation parameter…

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…

The standard definition of the Poisson brackets is generalized to the non-equal-time Poisson brackets. Their relationship to the equal-time Poisson brackets, as well as to the equal- and non-equal-time commutators, is discussed.

We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and Vinogradov, and we prove that…

We consider a class of \textit{factorizable} Poisson brackets which includes almost all reasonable Poisson structures. A particular case of the factorizable brackets are those associated with symplectic Lie algebroids. The BRST theory is…

A thorough analysis of Lie super-bialgebra structures on Lie super-algebras osp(1|2) and super-e(2) is presented. Combined technique of computer algebraic computations and a subsequent identification of equivalent structures is applied. In…

Given a symplectic form and a pseudo-riemannian metric on a manifold, a non degenerate even Poisson bracket on the algebra of differential forms is defined and its properties are studied. A comparison with the Koszul-Schouten bracket is…

Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on R^n taking values in a Grassmann algebra are described up to an equivalence transformation. It is shown that there are additional…

We study variuos homological structures associated with Poisson algebra, the canonical differential complex for singular Poisson structure and the analogue of the star operator for such manifolds. Give the interpretation of the classical…

We study the groups of local BRST cohomology associated to the general systems of ordinary differential equations, not necessarily Lagrangian or Hamiltonian. Starting with the involutive normal form of the equations, we explicitly compute…

In this paper, we describe double Poisson brackets in the sense of M. Van den Bergh on certain finite-dimensional algebras. In particular we prove that all possible double Poisson brackets on matrix algebras are "inner", i.e. given by some…

We explore variational Poisson-Nijenhuis structures on nonlinear PDEs and establish relations between Schouten and Nijenhuis brackets on the initial equation with the Lie bracket of symmetries on its natural extensions (coverings). This…

We show that the term `superdifferential equation' has been employed in the literature to refer to different types of differential equations with even and odd variables. It is justified on physical and mathematical grounds that a subclass…

The Schouten-Nijenhuis bracket is generalized for the superspace case and for the Poisson brackets of opposite Grassmann parities.

The Schouten bracket (or antibracket) plays a central role in the Poisson formalism and the Batalin-Vilkovisky quantization of gauge systems. There are several (in)equivalent ways to realize this concept on jet spaces. In this paper, we…

Requiring that a Lagrangian path integral leads to certain identities (Ward identities in a broad sense) can be formulated in a general BRST language, if necessary by the use of collective fields. The condition of BRST symmetry can then be…

We give a natural definition of a Poisson Differential Algebra. Consistence conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on differential calculus in a simple canonical form…

A set of consistent Poisson brackets for an open string in generic spacetime background and NS-NS $B$-field is constructed. Upon quantization, this set of Poisson brackets lead to spacial \emph{commutative} $D$-branes at the string ends,…

In this work we investigate connections between superalgebras and their realizations in terms of particles, branes and field theory models. We start from Poincar\'e superalgebras with brane charges and study its representations. The…

Some ideas relating to a bracket formulation for dissipative systems are considered. The formulation involves a bracket that is analogous to a generalized Poisson bracket, but possesses a symmetric component. Such a bracket is presented for…