Decomposition of (co)isotropic relations. (English) Zbl 1362.18005
For the study of the coisotropic relations between Poisson vector spaces, it is simplest to start with the case of isotropic relations between presymplectic spaces and pass by duality to the coisotropic relations between Poisson spaces [J. Lorand and A. Weinstein, SIGMA, Symmetry Integrability Geom. Methods Appl. 11, Paper 072, 10 p. (2015; Zbl 1327.15023)].
In section 2 is obtained the following result regarding isotropic relations: Any isotropic relation can be decomposed as the direct sum of a Cartesian relation and a biinjective relation both of which are isotropic.
Section 3 deals with decomposition of biinjective isotropic relations between presymplectic spaces.
In Section 4 is proved the main result: Any indecomposable isotropic relation between presymplectic vector spaces is isomorphic to exactly one relation from a list that contains 13 relations.
In section 2 is obtained the following result regarding isotropic relations: Any isotropic relation can be decomposed as the direct sum of a Cartesian relation and a biinjective relation both of which are isotropic.
Section 3 deals with decomposition of biinjective isotropic relations between presymplectic spaces.
In Section 4 is proved the main result: Any indecomposable isotropic relation between presymplectic vector spaces is isomorphic to exactly one relation from a list that contains 13 relations.
Reviewer: Cristian Lăzureanu (Timisoara)
MSC:
| 18B10 | Categories of spans/cospans, relations, or partial maps |
| 53D17 | Poisson manifolds; Poisson groupoids and algebroids |
| 17B63 | Poisson algebras |
Citations:
Zbl 1327.15023References:
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