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- W1995884237 abstract "In this paper we develop an abstract setup for hamiltonian group actions as follows: Starting with a continuous 2-cochain ω on a Lie algebra $${mathfrak h}$$ with values in an $${mathfrak h}$$ -module V, we associate subalgebras $${mathfrak {sp}(mathfrak h,omega) supseteq mathfrak {ham}(mathfrak h,omega)}$$ of symplectic, resp., hamiltonian elements. Then $${mathfrak {ham}(mathfrak h,omega)}$$ has a natural central extension which in turn is contained in a larger abelian extension of $${mathfrak {sp}(mathfrak h,omega)}$$ . In this setting, we study linear actions of a Lie group G on V which are compatible with a homomorphism $${mathfrak g to mathfrak {ham}(mathfrak h,omega)}$$ , i.e., abstract hamiltonian actions, corresponding central and abelian extensions of G and momentum maps $${J : mathfrak g to V}$$ ." @default.
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- W1995884237 date "2009-11-10" @default.
- W1995884237 modified "2023-10-18" @default.
- W1995884237 title "An abstract setting for hamiltonian actions" @default.
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- W1995884237 doi "https://doi.org/10.1007/s00605-009-0167-2" @default.
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