The moment maps in diffeology
Patrick Iglesias-zemmour
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
种类:
年:
2010
出版社:
Amer Mathematical Society
语言:
english
页:
85
ISBN 10:
0821847090
ISBN 13:
9780821847091
系列:
Memoirs of the American Mathematical Society 0972
文件:
PDF, 668 KB
IPFS:
,
english, 2010