A triplectic bi-Darboux theorem and para-hypercomplex geometry (Q2872417)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A triplectic bi-Darboux theorem and para-hypercomplex geometry |
scientific article; zbMATH DE number 6245491
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A triplectic bi-Darboux theorem and para-hypercomplex geometry |
scientific article; zbMATH DE number 6245491 |
Statements
A triplectic bi-Darboux theorem and para-hypercomplex geometry (English)
0 references
14 January 2014
0 references
bi-Poisson structures
0 references
para-hypercomplex geometry
0 references
Darboux coordinates
0 references
Poincaré lemma
0 references
triplectic manifolds
0 references
This work investigates the existence of bi-Darboux coordinates for triplectic manifolds. Let us recall that a bi-Poisson supermanifold is a supermanifold equipped with two Poisson brackets. In this paper, the authors provide necessary and sufficient conditions for the existence of bi-Darboux coordinates for bi-Poisson structures. The proof uses a new bi-Poincaré lemma with the help of \(\mathrm{sl}(2, \mathbb C)\) representation theory. The correspondence between triplectic manifolds and para-hypercomplex manifolds is also studied.
0 references
