Abstract
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.
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