For a symplectic manifold, the symplectomorphism group
is the subgroup of the diffeomorphism group of on the diffeomorphisms.
Analogous constructions apply when symplectic manifolds are generalized to n-plectic infinity-groupoids: for an n-plectic manifold, and -plectomorphism is a diffeomorphism that preserves the -plectic form .
A further subgroup is that of Hamiltonian symplectomorphisms. The group extension of that whose elements are pairs consisting of a Hamiltonian diffeomorphism and a choice of Hamiltonian for this is the quantomorphism group.
The Lie algebra of the symplectomorphism group is that of symplectic vector fields.
higher and integrated Kostant-Souriau extensions:
(∞-group extension of ∞-group of bisections of higher Atiyah groupoid for -principal ∞-connection)
(extension are listed for sufficiently connected )
Last revised on July 18, 2024 at 12:56:15. See the history of this page for a list of all contributions to it.