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Measures on groups of diffeomorphisms of non-archimedean Banach manifolds. (English. Russian original) Zbl 0897.46063

Russ. Math. Surv. 51, No. 2, 338-340 (1996); translation from Usp. Mat. Nauk 51, No. 2, 169-170 (1996).
The author adopts Bourbaki’s definition of a Banach manifold \(M\) over a non-archimedean valued field and considers separable subgroups \(G(t)\) of the group \(\text{ Diff}(t,M)\) of all automorphisms of \(M\) of smoothness class \(C(t)\). For such a \(G(t)\) a result on quasi-invariant measures is given. Further it is shown that the exponential map from the Lie algebra to the group is not locally bijective.

MSC:

46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
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