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Generalized Reduction Procedure: Symplectic and Poisson Formalism
Author(s) -
Grabowski J.,
Landi G.,
Marmo G.,
Vilasi G.
Publication year - 1994
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190420502
Subject(s) - symplectic geometry , formalism (music) , mathematics , pure mathematics , algebraic number , algebra over a field , reduction (mathematics) , commutative property , mathematical analysis , geometry , art , musical , visual arts
Abstract We present a generalized reduction procedure which encompasses the one based on the momentum map and the projection method. By using the duality between manifolds and ring of functions defined on them, we have cast our procedure in an algebraic context. In this framework we give a simple example of reduction in the non‐commutative setting.