Lyudkovskij, S. V. 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. Reviewer: M.van der Put (Groningen) Cited in 7 Documents MSC: 46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis Keywords:non-archimedean analysis; Haar measures; Bourbaki’s definition of a Banach manifold; non-archimedean valued field; exponential map; Lie algebra PDFBibTeX XMLCite \textit{S. V. Lyudkovskij}, Russ. Math. Surv. 51, No. 2, 338--340 (1996; Zbl 0897.46063); translation from Usp. Mat. Nauk 51, No. 2, 169--170 (1996) Full Text: DOI