An abstract setting for hamiltonian actions

作者：Neeb Karl Hermann; Vizman Cornelia^*

来源：Monatshefte fur Mathematik, 2010, 159(3): 261-288.

DOI：10.1007/s00605-009-0167-2

• Central extension
• Momentum map
• Hamiltonian action
• Abelian extension
• Infinite dimensional Lie group

In this paper we develop an abstract setup for hamiltonian group actions as follows: Starting with a continuous 2-cochain omega on a Lie algebra h with values in an h-module V, we associate subalgebras sp(h, omega) superset of ham(h, omega) of symplectic, resp., hamiltonian elements. Then ham(h, omega) has a natural central extension which in turn is contained in a larger abelian extension of sp(h, omega). In this setting, we study linear actions of a Lie group G on V which are compatible with a homomorphism g -> ham(h, omega), i. e., abstract hamiltonian actions, corresponding central and abelian extensions of G and momentum maps J : g -> V.

• 出版日期2010-2