L-infinity bialgebroids and homotopy Poisson structures on supermanifolds
@article{Voronov2019LinfinityBA, title={L-infinity bialgebroids and homotopy Poisson structures on supermanifolds}, author={Theodore Th. Voronov}, journal={arXiv: Differential Geometry}, year={2019} }
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 $L_{\infty}$-bialgebroid. (Higher Koszul brackets on forms introduced earlier by H. Khudaverdian and the author are part of one of its manifestations.) The underlying general construction is that of a "(quasi)triangular" $L_{\infty}$-bialgebroid, which is…
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References
SHOWING 1-10 OF 16 REFERENCES
On homotopy Lie bialgebroids
- Mathematics
- 2016
A well-known result of A. Vaintrob characterizes Lie algebroids and their morphisms in terms of homological vector fields on supermanifolds. We give an interpretation of Lie bialgebroids and their…
Homotopy Loday Algebras and Symplectic $2$-Manifolds
- Mathematics
- 2018
Using the technique of higher derived brackets developed by Voronov, we construct a homotopy Loday algebra in the sense of Ammar and Poncin associated to any symplectic $2$-manifold. The algebra we…
Thick morphisms, higher Koszul brackets, and $L_{\infty}$-algebroids
- Mathematics
- 2018
It is a classical fact in Poisson geometry that the cotangent bundle of a Poisson manifold has the structure of a Lie algebroid. Manifestations of this structure are the Lichnerowicz differential on…
The "nonlinear pullback" of functions and a formal category extending the category of supermanifolds
- Mathematics
- 2014
We introduce mappings between function spaces on smooth (super)manifolds, which are generally nonlinear and which generalize the pullbacks with respect to smooth maps. The construction uses canonical…
Microformal Geometry and Homotopy Algebras
- MathematicsProceedings of the Steklov Institute of Mathematics
- 2018
We extend the category of (super)manifolds and their smooth mappings by introducing a notion of microformal, or “thick,” morphisms. They are formal canonical relations of a special form, constructed…
Graded Geometry, Q‐Manifolds, and Microformal Geometry
- MathematicsFortschritte der Physik
- 2019
We give an exposition of graded and microformal geometry, and the language of Q‐manifolds. Q‐manifolds are supermanifolds endowed with an odd vector field of square zero. They can be seen as a…
Graded Manifolds and Drinfeld Doubles for Lie Bialgebroids
- Mathematics
- 2001
We define graded manifolds as a version of supermanifolds endowed with an extra Z-grading in the structure sheaf, called weight (not linked
with parity). Examples are ordinary supermanifolds, vector…
Lie bialgebroids and Poisson groupoids
- Mathematics
- 1994
Lie bialgebras arise as infinitesimal invariants of Poisson Lie groups. A Lie bialgebra is a Lie algebra g with a Lie algebra structure on the dual g∗ which is compatible with the Lie algebra g in a…