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Conjugacy in inverse semigroups
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Orientador(es)
Resumo(s)
In a group G, elements a and b are conjugate if there exists g∈G such that g−1ag=b. This conjugacy relation, which plays an important role in group theory, can be extended in a natural way to inverse semigroups: for elements a and b in an inverse semigroup S, a is conjugate to b, which we will write as a∼ib, if there exists g∈S1 such that g−1ag=b and gbg−1=a. The purpose of this paper is to study the conjugacy ∼i in several classes of inverse semigroups: symmetric inverse semigroups, McAllister P-semigroups, factorizable inverse monoids, Clifford semigroups, the bicyclic monoid, stable inverse semigroups, and free inverse semigroups.
Descrição
The first and second authors were partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matematica e Aplicacoes), the project PTDC/MHC-FIL/2583/2014, the FCT project PTDC/MAT-PUR/31174/2017.
The second author was also partially supported by a Simons Foundation Collaboration Grant 359872.
Palavras-chave
Bicyclic monoid Clifford semigroups Conjugacy Factorizable inverse monoids Free inverse semigroups Inverse semigroups McAllister P-semigroups Stable inverse semigroups Symmetric inverse semigroups Algebra and Number Theory