Related papers: Courant algebroids and Poisson Geometry

We construct an infinite dimensional Lie rackoid Y which hosts an integration of the standard Courant algebroid. As a set, Y = C $\infty$ ([0, 1], T * M) for a compact manifold M. The rackoid product is by automorphisms of the Dorfman…

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras…

We show that the skew-symmetrized product on every Leibniz algebra E can be realized on a reductive complement to a subalgebra in a Lie algebra. As a consequence, we construct a nonassociative multiplication on E which, when E is a Lie…

Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular somehow unexpected…

Li-Bland's correspondence between linear Courant algebroids and Lie $2$-algebroids is explained and shown to be an equivalence of categories. Decomposed VB-Courant algebroids are shown to be equivalent to split Lie 2-algebroids in the same…

We study polynomial Poisson algebras with some regularity conditions. Linear (Lie-Berezin-Kirillov) structures on dual spaces of semi-simple Lie algebras, quadratic Sklyanin elliptic algebras of \cite{FO1},\cite{FO2} as well as polynomial…

We define prequantization for Dirac manifolds to generalize known procedures for Poisson and (pre) symplectic manifolds by using characteristic distributions obtained from 2-cocycles associated to Dirac structures. Given a Dirac manifold…

We study multiplicative quiver varieties associated to specific extensions of cyclic quivers with $m\geq 2$ vertices. Their global Poisson structure is characterised by quasi-Hamiltonian algebras related to these quivers, which were studied…

We consider higher generalizations of both a (twisted) Poisson structure and the equivariant condition of a momentum map on a symplectic manifold. On a Lie algebroid over a (pre-)symplectic and (pre-)multisymplectic manifold, we introduce a…

We extend the Poisson bracket from a Lie bracket of phase space functions to a Lie bracket of functions on the space of canonical histories and investigate the resulting algebras. Typically, such extensions define corresponding Lie algebras…

Given a symplectic manifold $M$, we may define an operad structure on the the spaces $\op^k$ of the Lagrangian submanifolds of $(\bar{M})^k\times M$ via symplectic reduction. If $M$ is also a symplectic groupoid, then its multiplication…

A study of sigma models whose target space is a group G that admits a compatible Poisson structure is presented. The natural action of O(D,D;Z) on the generalised tangent bundle TG+T*G and a generalisation of the Courant bracket that…

In this paper, we introduce the notion of $E$-Courant algebroids, where $E$ is a vector bundle. It is a kind of generalized Courant algebroid and contains Courant algebroids, Courant-Jacobi algebroids and omni-Lie algebroids as its special…

Let p be a maximal truncated parabolic subalgebra of a simple Lie Algebra. It was shown in many cases that the Poisson centre Y(p) is a polynomial algebra. We construct a slice for the coadjoint action of p, thus extending a theorem of…

We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a…

In this paper, first we modify the definition of a Hom-Lie algebroid introduced by Laurent-Gengoux and Teles and give its equivalent dual description. Many results that parallel to Lie algebroids are given. In particular, we give the notion…

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an L-infinity algebra, which we construct explicitly. Our machinery is based on Th. Voronov's derived bracket…

Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely…

This article presents a differential groupoid with ``coaction'' of the groupoid underlying the Quantum Euclidean Group (i.e. its $C^*$-algebra is the $C^*$-algebra of this quantum group). The dual of the Lie algebroid is a Poisson manifold…

We introduce and study some mixed product Poisson structures on product manifolds associated to Poisson Lie groups and Lie bialgebras. For quasitriangular Lie bialgebras, our construction is equivalent to that of fusion products of…