Local Smooth Conjugations of Frobenius Endomorphisms

A generalization of the Böttcher equation is considered. It turned out that the parametrized Poisson integral, as a function of its parameters, satisfies an equation of the type described. The structure theorem for splitting maps of Frobenius endomorphisms in a ring and in an algebra over it is prov...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-12, Vol.251 (4), p.503-511
Main Authors: Kalnitsky, V. S., Petrov, A. N.
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
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Summary:A generalization of the Böttcher equation is considered. It turned out that the parametrized Poisson integral, as a function of its parameters, satisfies an equation of the type described. The structure theorem for splitting maps of Frobenius endomorphisms in a ring and in an algebra over it is proved. The real field case is considered. The generalized Böttcher equation is solved for classical two-dimensional algebras and for the Poisson algebra.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-05109-0