The Moment Maps in Diffeology

Patrick Iglesias-Zemmour (Autor)

Buch | Softcover

72 Seiten

2010
American Mathematical Society (Verlag)
978-0-8218-4709-1 (ISBN)

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Presents a generalization of the moment maps to the category /{$Diffeology$/}. This construction applies to every smooth action of any diffeological group /textup{G} preserving a closed 2-form /omega, defined on some diffeological space /textup{X}. In particular, that reveals a universal construction, associated to the action of the whole group of automorphisms /mathrm{Diff}(/textup{X},/omega).

This memoir presents a generalization of the moment maps to the category /{$Diffeology$/}. This construction applies to every smooth action of any diffeological group /textup{G} preserving a closed 2-form /omega, defined on some diffeological space /textup{X}. In particular, that reveals a universal construction, associated to the action of the whole group of automorphisms /mathrm{Diff}(/textup{X},/omega). By considering directly the space of momenta of any diffeological group /textup{G}, that is the space /mathscr{G}^* of left-invariant 1-forms on /textup{G}, this construction avoids any reference to Lie algebra or any notion of vector fields, or does not involve any functional analysis. These constructions of the various moment maps are illustrated by many examples, some of them originals and others suggested by the mathematical literature.

Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Gewicht	455 g
Themenwelt	Mathematik / Informatik ► Mathematik
ISBN-10	0-8218-4709-0 / 0821847090
ISBN-13	978-0-8218-4709-1 / 9780821847091
Zustand	Neuware