相关论文: Derived Brackets from Super-Poisson Brackets

We review the linearization of Poisson brackets and related problems, in the formal, analytic and smooth categories.

We compute the Poisson bracket relations for the monodromy matrix of the auxiliary linear problem. If the basic Poisson bracket relations of the model contain derivatives, this computation leads to a peculiar type of symmetry breaking which…

In this paper we construct a non-skewsymmetric version of a Poisson bracket on the algebra of smooth functions on an odd Jacobi supermanifold. We refer to such Poisson-like brackets as Loday-Poisson brackets. We examine the relations…

In this note the notion of Poisson brackets in Kontsevich's "Lie World" is developed. These brackets can be thought of as "universally" defined classical Poisson structures, namely formal expressions only involving the structure maps of a…

Supersymmetric nonlinear sigma models have target spaces that carry interesting geometry. The geometry is richer the more supersymmetries the model has. The study of models with two dimensional world sheets is particularly rewarding since…

On a Poisson manifold endowed with a Riemannian metric we will construct a vector field that generalizes the double bracket vector field defined on semi-simple Lie algebras. On a regular symplectic leaf we will construct a generalization of…

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…

A vertical exterior derivative is constructed that is needed for a graded Poisson structure on multisymplectic manifolds over nontrivial vector bundles. In addition, the properties of the Poisson bracket are proved and first examples are…

Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with a non-degenerate Poisson…

Hartwig, Larsson and the second author in [J. Algebra, 2005] defined a bracket on sigma-derivations of a commutative algebra. We show that this bracket preserves inner derivations, and based on this obtain some structural results on…

This note gives an overview on the construction of symplectic groupoids as reduced phase spaces of Poisson sigma models and its generalization in the infinite dimensional setting (before reduction).

We analyse the problem of boundary conditions for the Poisson-Sigma model and extend previous results showing that non-coisotropic branes are allowed. We discuss the canonical reduction of a Poisson structure to a submanifold, leading to a…

Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a…

A large class of supersymmetric extended objects is considered from the viewpoint of embeddings of super worldsurfaces into target superspaces. It is shown that a simple geometrical condition leads to the equations of motion for the brane…

Non commutative superspaces can be introduced as the Moyal-Weyl quantization of a Poisson bracket for classical superfields. Different deformations are studied corresponding to constant background fields in string theory. Supersymmetric and…

We study the worldsheet theory of bosonic string from the point of view of the BV formalism. We explicitly describe the derived Poisson structure which arizes when we expand the Master Action near a Lagrangian submanifold. The BV formalism…

We give a review of brackets and interior products in bosonic string theory, in different representations, used in formulation of a theory and derived in a transformation of related mathematical structures. We consider the C-bracket,…

In the first part the sh Lie structure of brackets in field theory, described in the jet bundle context along the lines suggested by Gel'fand, Dickey and Dorfman, is analyzed. In the second part, we discuss how this description allows us to…

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 develop the theory of double multiplicative Poisson vertex algebras. These structures, defined at the level of associative algebras, are shown to be such that they induce a classical structure of multiplicative Poisson vertex algebra on…