Related papers: Transitive Courant algebroids

This paper contributes to the characterization of a certain class of commutative Hopf algebroids. It is shown that a commutative flat Hopf algebroid with a non zero base ring and a nonempty character groupoid is geometrically transitive if…

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 paper we introduce and study some mathematical structures on top of transitive Lie algebroids in order to formulate gauge theories in terms of generalized connections and their curvature: metrics, Hodge star operator and integration…

Let E be a transitive Courant algebroid with scalar product of neutral signature. A generalized almost complex structure \mathcal J on E is a skew-symmetric smooth field of endomorphisms of E which squares to minus the identity. We say that…

We present a classification of transitive vertex algebroids on a smooth variety X carried out in the spirit of Bressler's classification of Courant algebroids. In particular, we compute the class of the stack of transitive vertex…

We introduce the notion of hypersymplectic structure on a Courant algebroid and we prove the existence of a one-to-one correspondence between hypersymplectic and hyperk\"ahler structures. This correspondence provides a simpler way to define…

This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles (E\to M_{0}) by canonically associating…

The concept of algebroid is convenient for constructions of geometrical frameworks. For example, metric-affine and generalized geometries can be written on Lie and Courant algebroids, respectively. Furthermore, string theories might make…

Given a vector bundle $A$ over a smooth manifold $M$ such that the square root $\mathcal{L}$ of the line bundle $\wedge^{\mathrm{top}}A^\ast \otimes \wedge^{\mathrm{top}}T^\ast M$ exists, the Clifford bundle associated to the split…

A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of…

We study Hamiltonian spaces associated with pairs (E,A), where E is a Courant algebroid and A\subset E is a Dirac structure. These spaces are defined in terms of morphisms of Courant algebroids with suitable compatibility conditions.…

The core diagram of a double Lie algebroid consists in the core of the double Lie algebroid, together with the two core-anchor maps to the sides of the double Lie algebroid. If these two core anchors are surjective, then the double Lie…

This paper introduces a method for constructing pure algebroids, dull algebroids, and Lie algebroids. The construction relies on what we deffned as n-systems on vector bundles, and we provide explicit computations for all resulting…

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…

For any regular Courant algebroid, we construct a characteristic class a la Chern-Weil. This intrinsic invariant of the Courant algebroid is a degree-3 class in its naive cohomology. When the Courant algebroid is exact, it reduces to the…

Let \(X\) be an irreducible smooth complex projective variety, and let \(G\) be a connected reductive linear algebraic group over \(\mathbb{C}\). In this paper, we first classify integrable transitive algebraic Lie algebroids on $X$. We…

We define a Courant bracket on an associative algebra using the theory of Hochschild homology, and we introduce the notion of Dirac algebra. We show that the bracket of an omni-Lie algebra is quite a kind of Courant bracket.

For any transversal-Courant algebroid $E$ on a foliated manifold $(M,\mathcal{F})$, and for any choice of a decomposition $TM=T\mathcal{F}\oplus Q$, we construct a Courant algebroid structure on $T\mathcal{F}\oplus T^*\mathcal{F}\oplus E$.

Shifted symplectic Lie and $L_\infty$ algebroids model formal neighbourhoods of manifolds in shifted symplectic stacks, and serve as target spaces for twisted variants of classical AKSZ topological field theory. In this paper, we classify…

In our previous paper (arXiv:1306.5449) we have given a sufficient and necessary condition when the coupling between Lie algebra bundle (LAB) and the tangent bundle exists in the sense of Mackenzie (\cite{Mck-2005}, Definition 7.2.2) for…