Tight Representations of 0-E-Unitary Inverse Semigroups

Abstract EN

We study the tight representation of a semilattice in {0,1} by some examples.

Then we introduce the concept of the complex tight representation of an inverse semigroup S by the concept of the tight representation of the semilattice of idempotents E of S in {0,1}.

Specifically we describe the tight representation of a 0-E-unitary inverse semigroup and prove that if σ is a tight semilattice representation of the 0-E-unitary inverse semigroup S in {0,1}, then σ is a complex tight representation.