Cross-connections in Clifford semigroups
Group Theory
2022-08-02 v1 Category Theory
Abstract
An inverse Clifford semigroup (often referred to as just a Clifford semigroup) is a semilattice of groups. It is an inverse semigroup and in fact, one of the earliest studied classes of semigroups. In this short note, we discuss various structural aspects of a Clifford semigroup from a cross-connection perspective. In particular, given a Clifford semigroup, we show that the semigroup of normal cones is isomorphic to the original semigroup, even when it is not a monoid. Hence, we see that cross-connection description degenerates in Clifford semigroups. Further, we specialise the discussion to provide the description of the cross-connection structure in an arbitrary semilattice, also.
Cite
@article{arxiv.2208.00143,
title = {Cross-connections in Clifford semigroups},
author = {P. A. Azeef Muhammed and C. S. Preenu},
journal= {arXiv preprint arXiv:2208.00143},
year = {2022}
}