Related papers: Hyperstructures on Lie algebroids
We develop a theory of quasi-Lie bialgebroids using a homological approach. This notion is a generalization of quasi-Lie bialgebras, as well as twisted Poisson structures with a 3-form background which have recently appeared in the context…
We give a notion of compatibility between a Riemannian metric and a Jacobi structure. We prove that in case of Poisson structures, contact structures and locally conformally symplectic structures, fundamental examples of Jacobi structures,…
The link between (super)-affine Lie algebras as Poisson brackets structures and integrable hierarchies provides both a classification and a tool for obtaining superintegrable hierarchies. The lack of a fully systematic procedure for…
A hypersymplectic structure on a 4-manifold is a triple $\omega_1, \omega_2, \omega_3$ of 2-forms for which every non-trivial linear combination $a^1\omega_1 + a^2 \omega_2 + a^3 \omega_3$ is a symplectic form. Donaldson has conjectured…
In this paper, we extend the concept of Lie superalgebras to a more generalized framework called Super-Lie superalgebras. In addition, they seem to be exploring various supergeneralizations of other algebraic structures, such as…
The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified and the corresponding symplectic forms are…
We revisit and construct new examples of supersymmetric 2D topological sigma models whose target space is a Poisson supermanifold. Inspired by the AKSZ construction of topological field theories, we follow a graded-geometric approach and…
The theory of Nambu-Poisson structures on manifolds is extended to the context of Lie algebroids, in a natural way based on the Vinogradov bracket associated with Lie algebroid cohomology. We show that, under certain assumptions, any…
This short note provides a symplectic analogue of Vaisman's theorem in complex geometry. Namely, for any compact symplectic manifold satisfying the hard Lefschetz condition in degree 1, every locally conformally symplectic structure is in…
We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…
We complete the construction of the double Lie algebroid of a double Lie groupoid begun in the first paper of this title. We show that the Lie algebroid structure of an LA--groupoid may be prolonged to the Lie algebroid of its Lie groupoid…
Using Fedosov's approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In the case of Kaehler-Poisson manifolds this construction…
In this paper, we introduce right-invariant (similarly, left-invariant) Poisson-Nijenhuis Structures on Lie groupoids and their infinitesimal counterparts as called $(\Lambda , \mathbf{n})-$structures. We present a mutual correspondence…
We investigate Nijenhuis deformations of $L_\infty$-algebras, a notion that unifies several Nijenhuis deformations, namely those of Lie algebras, Lie algebroids, Poisson structures and Courant structures. Additional examples, linked to Lie…
We generalize to the homotopy case a result of K. Mackenzie and P. Xu on relation between Lie bialgebroids and Poisson geometry. For a homotopy Poisson structure on a supermanifold $M$, we show that $(TM, T^*M)$ has a canonical structure of…
An explicit classification of homogeneous quaternionic Kaehler structures by real tensors is derived and we relate this to the representation-theoretic description found by Fino. We then show how the quaternionic hyperbolic space HH(n) is…
We provide explicit formulas for integrating multiplicative forms on local Lie groupoids in terms of infinitesimal data. Combined with our previous work [8], which constructs the local Lie groupoid of a Lie algebroid, these formulas produce…
Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the…
A manifold is said to be $n$-plectic if it is equipped with a closed, nondegenerate $(n+1)$-form. This thesis develops the theory of \emph{relative $n$-plectic structures}, where the classical condition is replaced by a closed,…
This work concerns the definition and analysis of a new class of Lie systems on Poisson manifolds enjoying rich geometric features: the Lie--Hamilton systems. We devise methods to study their superposition rules, time independent constants…