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- W1987275870 abstract "ABSTRACT. For a symplectic manifold M and its associated real Lie algebraP(M, io) (its Poisson algebra) a definition of firsVorder representations and astructure theorem for the representation ring is given. 0. In physics and in the context of geometric quantization, the term prequan-tization is used to denote a special kind of representation of the Poisson algebraP(M, ui). Here, we give a more general and natural definition of representations of the Lie algebra P(M,u>) (Definition 1) and show, how prequantizations fit into this scheme, and we finally compute the representation ring (Propositions 4, 5). We relyon some facts on prequantizations, which can be found in [1, 2, 3]; as for differentialoperators, we refer to [4].1. In the sequel we need the following statements on prequantization. Let (M, ui)denote a symplectic manifold, i.e. a paracompact, connected, real C°°-manifold of dimension n carrying a regular and closed 2-form w; let C°°(M) denote the ringof real valued C°°-functions on M. Every / G ^(M) has its Hamilton field Vf G" @default.
- W1987275870 created "2016-06-24" @default.
- W1987275870 creator A5037207184 @default.
- W1987275870 date "1982-03-01" @default.
- W1987275870 modified "2023-09-24" @default.
- W1987275870 title "Representing triples of a symplectic manifold" @default.
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- W1987275870 doi "https://doi.org/10.1090/s0002-9939-1982-0671196-0" @default.
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