Journal of Mathematical Extension (Jun 2009)
C ∗ -Algebra of Cancellative Semigroupoids
Abstract
In this paper the definition and some properties of semigroupoids are considered. Representations, tight representations, and universal representations of a cancellative semigroupoid are discussed. Also, the C ∗ -algebra of a semigroupoid is introduced and it is shown that source elements transfer to zero by tight representations.