Strong Morita Equivalence of Inverse Semigroups

Details Strong Morita Equivalence of Inverse Semigroups Strong Morita Equivalence of Inverse Semigroups

2009-01-18

arxiv.org/abs/0901.2696v1

Mathematics

Operator Algebras

Scientific paper

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 $C^*$-algebras. As a consequence we obtain a new proof of a result of Khoshkam and Skandalis showing that the $C^*$-algebra of an $F$-inverse semigroup is strongly Morita equivalent to a cross product of a commutative $C^*$-algebra by a group.

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