相关论文: Derived Brackets from Super-Poisson Brackets
The purpose of this work is to study Lie superalgebroid structures on the space of superdifferential $1$-forms over the supermanifolds whose superfunctions are the differential forms on its underlying manifold. These superalgbroids are…
We construct Poisson bracket relations between the operators which generate the chiral ring of the Coulomb branch of certain $3d$ $\mathcal{N}=4$ quiver gauge theories. In the case where the Coulomb branch is a free space, $ADE$ Klein…
A dynamical symmetry for supersymmetric extended objects is given.
We consider features of the Hamiltonian formulation of the Whitham method in the presence of pseudo-phases. As we show, an analog of the procedure of averaging of the Poisson bracket with the reduced number of the first integrals can be…
We complete the derived equivalence classification of all symmetric algebras of polynomial growth, by solving the subtle problem of distinguishing the standard and nonstandard nondomestic symmetric algebras of polynomial growth up to…
We consider supersymmetrization of Hamiltonian dynamics via antibrackets for systems whose Hamiltonian generates an isometry of the phase space. We find that the models are closely related to the supersymmetric non-linear $\sigma$-model. We…
We analyse the general boundary conditions (branes) consistent with the Poisson-sigma model and study the structure of the phase space of the model defined on the strip with these boundary conditions. Finally, we discuss the perturbative…
Recent work has shown that two-dimensional non-linear $\sigma$-models on group manifolds with Poisson-Lie symmetry can be understood within generalised geometry as exemplars of generalised parallelisable spaces. Here we extend this idea to…
In this contribution we review some of the interplay between sigma models in theoretical physics and novel geometrical structures such as Lie (n-)algebroids. The first part of the article contains the mathematical background, the definition…
In this paper, we describe the dynamical symmetries of classical supersymmetric oscillators in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket which is defined as a suitable classical…
We investigate the relation between supersymmetry and geometry for two dimensional sigma models with target spaces of arbitrary signature, and Lorentzian or Euclidean world-sheets. In particular, we consider twisted forms of the…
It is shown that the dual of the double compactified D=11 Supermembrane and a suitable compactified D=10 Super 4D-brane with nontrivial wrapping on the target space may be formulated as noncommutative gauge theories. The Poisson bracket…
Let Spec(A) be an affine derived stack. We give two proofs of the existence of a canonical map from the moduli space of shifted Poisson structures (in the sense of Pantev-To\"en-Vaqui\'e-Vezzosi, see http://arxiv.org/abs/1111.3209 ) on…
The Poisson sigma model is a widely studied two-dimensional topological field theory. This note shows that boundary conditions for the Poisson sigma model are related to coisotropic submanifolds (a result announced in [math.QA/0309180]) and…
The aim of this paper is to study some brackets defined on $(\tau,\sigma)$-derivations satisfying quasi-Lie identities. Moreover, we provide examples of $(p,q)$-deformations of Witt and Virasoro algebras as well as $\mathfrak{sl}(2)$…
The algebraic and geometric classification of all complex $3$-dimensional transposed Poisson algebras is obtained. Also, we discuss strong special $3$-dimensional transposed Poisson algebras.
We introduce coupled double Poisson brackets on an associative algebra $A$ as pairs consisting of a generalized Van den Bergh's double Poisson bracket and a generalized Fairon--McCulloch's right double Poisson bracket subject to a…
We establish a link between the multisymplectic and the covariant phase space approach to geometric field theory by showing how to derive the symplectic form on the latter, as introduced by Crnkovic-Witten and Zuckerman, from the…
We present a comprehensive study of two new Poisson-type algebras. Namely, we are working with $\delta$-Poisson and transposed $\delta$-Poisson algebras. Our research shows that these algebras are related to many interesting identities. In…
We give a construction of homotopy algebras based on ``higher derived brackets''. More precisely, the data include a Lie superalgebra with a projector on an Abelian subalgebra satisfying a certain axiom, and an odd element $\Delta$. Given…