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A generalized global differential calculus. II: Application to invariance under a Lie group. (English) Zbl 0613.58004
A generalized setting for developing the theory of Lie groups is provided. In particular, for an element c of a G-set, if c is a local invariant with ”invariant domain” and G is connected, c is seen to be invariant. Local invariants are seen to coincide with infinitesimal variants and the formula \[ D_{[\theta,x]} = [D_{\theta},D_ x] \] shown. For this formula lower order terms of power series expansions are considered. The author’s approach is more systematic and general than the usual ones, especially with respect to domains of definition.
Reviewer: P.Cheremack
MSC:
58B25 Group structures and generalizations on infinite-dimensional manifolds
22E20 General properties and structure of other Lie groups
18F15 Abstract manifolds and fiber bundles (category-theoretic aspects)
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