English

Strong Morita Equivalence of Inverse Semigroups

Operator Algebras 2009-01-20 v1 Category Theory Group Theory

Abstract

We introduce strong Morita equivalence for inverse semigroups. This notion encompasses Mark Lawson's concept of enlargement. Strongly Morita equivalent inverse semigroups have Morita equivalent universal groupoids in the sense of Paterson and hence strongly Morita equivalent universal and reduced CC^*-algebras. As a consequence we obtain a new proof of a result of Khoshkam and Skandalis showing that the CC^*-algebra of an FF-inverse semigroup is strongly Morita equivalent to a cross product of a commutative CC^*-algebra by a group.

Keywords

Cite

@article{arxiv.0901.2696,
  title  = {Strong Morita Equivalence of Inverse Semigroups},
  author = {Benjamin Steinberg},
  journal= {arXiv preprint arXiv:0901.2696},
  year   = {2009}
}