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Reversibility and transitivity of semigroup actions on homogeneous spaces

Part of: Semigroups Connections with other structures, applications Noncompact transformation groups

Published online by Cambridge University Press:  24 February 2025

Ronan A. Reis ,
Luiz A. B. San Martin  and
Victor H. L. Rocha
Ronan A. Reis
Affiliation:
Departamento de Matemática e Computação, Universidade Estadual Paulista, R. Roberto Simonsen, 305, 19060900, Presidente Prudente, Brazil e-mail: ronan.reis@unesp.br
Luiz A. B. San Martin
Affiliation:
Instituto de Matemática, Universidade Estadual de Campinas, Estatística e Computação Científica, Cx. Postal 6065, 13081970, Campinas, Brazil e-mail: smartin@unicamp.br
Victor H. L. Rocha*
Affiliation:
Departamento de Matemática e Computação, Universidade Estadual Paulista, R. Roberto Simonsen, 305, 19060900, Presidente Prudente, Brazil e-mail: ronan.reis@unesp.br
*
e-mail: rocha.vhl@gmail.com
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Abstract

This paper studies reversibility and transitivity of semigroups acting on homogeneous spaces. Properties of the reversor set of a subsemigroup acting on homogeneous spaces are presented. Let G be a topological group and L a subgroup of G. Assume that S is a subsemigroup of G with nonempty interior. It is presented a study of the reversibility of the S-action on $G/L$ in terms of the actions of S and L on homogeneous spaces of G. The results relate the reversibility and the transitivity of S in $G/L$ with the minimality of the action of L on homogeneous spaces of G. In addition, sufficient conditions for S to be right reversible in G if S is reversible in $G/L$ are presented.

Keywords

Semigroup actionsreversibilitytransitivityhomogeneous spacesequivariant fibrations

MSC classification

Primary: 54H15: Transformation groups and semigroups 20M20: Semigroups of transformations, etc. 22F30: Homogeneous spaces
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 20
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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