Related papers: Courant-like brackets and loop spaces
Poisson structures related with the affine Courant type algebroid are analyzed, including \ those related with cotangent bundles on Lie group manifolds. A special attantion is paid to Courant type algebroids and related R-structures \ on…
We introduce a new type of algebra, the Courant-Dorfman algebra. These are to Courant algebroids what Lie-Rinehart algebras are to Lie algebroids, or Poisson algebras to Poisson manifolds. We work with arbitrary rings and modules, without…
The purpose of this paper is to discuss a number of issues that crop up in the computation of Poisson brackets in field theories. This is specially important for the canonical approaches to quantization and, in particular, for loop quantum…
The formulation of covariant brackets on the space of solutions to a variational problem is analyzed in the framework of contact geometry. It is argued that the Poisson algebra on the space of functionals on fields should be read as a…
This paper is devoted to studying some properties of the Courant algebroids: we explain the so-called "conducting bundle construction" and use it to attach the Courant algebroid to Dixmier-Douady gerbe (following ideas of P. Severa). We…
A common approach to the theory of nonlocal Poisson brackets, seen from the operatorial point of view, has been to keep implicit the sets on which these brackets act. In this paper we aim to explicitly define appropriate functional spaces…
In this paper, we consider a notion of a higher version of the relation between Courant-Dorfman algebras and Poisson vertex algebras. We define a higher Courant-Dorfman algebra, and study the relationship with graded symplectic geometry. In…
If $A$ is a Lie algebroid over a foliated manifold $(M,\mathcal{F})$, a foliation of $A$ is a Lie subalgebroid $B$ with anchor image $T\mathcal{F}$ and such that $A/B$ is locally equivalent with Lie algebroids over the slice manifolds of…
Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the direct sum of tangent and cotangent bundles with the bracket introduced by T. Courant for the study of Dirac structures. Within the category…
In the context of generalized geometry we first show how the Courant bracket helps to define connections with skew torsion and then investigate a five-dimensional invariant functional and its associated geometry. A Hamiltonian flow arising…
We study certain Poisson structures related to quantized enveloping algebras. In particular, we give a description of the Poisson structure of a certain manifold associated to the ring of differential operators.
The covariant canonical formalism is a covariant extension of the traditional canonical formalism of fields. In contrast to the traditional canonical theory, it has a remarkable feature that canonical equations of gauge theories or gravity…
In this dissertation we study Courant algebroids, objects that first appeared in the work of T. Courant on Dirac structures; they were later studied by Liu, Weinstein and Xu who used Courant algebroids to generalize the notion of the…
The binary bracket of a Courant algebroid structure on $(E,\langle \cdot,\cdot \rangle)$ can be extended to a $n$-ary bracket on $\Gamma(E)$, yielding a multi-Courant algebroid. These $n$-ary brackets form a Poisson algebra and were…
We study a new kind of Courant algebroid on Poisson manifolds, which is a variant of the generalized tangent bundle in the sense that the roles of tangent and the cotangent bundle are exchanged. Its symmetry is a semidirect product of…
In this thesis we develop the notion of LA-Courant algebroids, the infinitesimal analogue of multiplicative Courant algebroids. Specific applications include the integration of q- Poisson (d, g)-structures, and the reduction of Courant…
In this paper we consider structures of complex Poisson brackets on the space of smooth functions in a $n$-dimensional complex manifold generated by the $(1,1)$-form $d=\partial+\overline{\partial}$-closed and non-degenerate (with…
In this work, we find the Poisson superalgebras related to schemes of quantization. Initially, we consider the Dirac superbracket in the context of the quantization of constrained systems. Next, we show the existence of a Poisson…
The correspondence between Poisson structures and symplectic groupoids, analogous to the one of Lie algebras and Lie groups, plays an important role in Poisson geometry; it offers, in particular, a unifying framework for the study of…
We provide a short review of Courant algebroids and graded symplectic manifolds and show how different Courant algebroids emerge from double field theory. Fluxes of double field theory and their Bianchi identities are formulated by using…