Casey Blacker, Augusta University
Geometric and algebraic reduction of multisymplectic manifolds
A symplectic Hamiltonian manifold consists of a Lie group action on a symplectic manifold together with an associated moment map. In special cases, the moment map distinguishes a smooth submanifold to which the Lie group action restricts, and the quotient inherits the structure of a symplectic manifold. In every case, it is possible to construct a reduced Poisson algebra that plays the role of the space of smooth functions on the reduced space.
In this talk, we will discuss an adaptation of these ideas to the multisymplectic setting. Specifically, we will exhibit a geometric reduction scheme for multisymplectic manifolds in the presence of a Hamiltonian action, an algebraic reduction procedure for the associated L-infinity algebras of classical observables, and a comparison of these two constructions. This is joint work with Antonio Miti and Leonid Ryvkin.
MC 5417