Tue, 7 Mar 2023, 1:25 pm MST
The conjugacy equivalence relation in groups can be generalized to semigroups in various
distinct ways. For example, in an inverse monoid $S$, one might define $a,b\in S$ to
be conjugate if there exists $g\in S$ such that $g^{-1}ag = b$ and $gbg^{-1} = a$. There
are other semigroup generalizations of conjugacy which do not involve inverses at all.
In this talk I will survey the various generalizations, focusing particularly on a notion
known as natural conjugacy, which, in inverse semigroups, coincides with the one defined
above. Along the way, I will discuss connections with partial inner automorphisms and with the
(universal algebra) center of an inverse semigroup.
The work described herein is joint with
J. Araújo, W. Bentz, J. Konieczny, A. Malheiro, V. Mercier and D. Stanovský.
[video]