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Reversibility and transitivity of semigroup actions on homogeneous spaces

Year: 2025

Type: article

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.

Source: Canadian Journal of Mathematics

DOI: 10.4153/s0008414x24001044

Authors: Ronan A. Reis, Luiz A. B. San Martin, Victor H. L. Rocha

Institutions: Universidade Estadual Paulista (Unesp), Universidade Estadual de Campinas (UNICAMP)

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4407888648

FWCI:

Cites: 17

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Related to: 10