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C*-algebras from partial isometric representations of LCM semigroups (2001.00156v4)
Published 1 Jan 2020 in math.OA, math.CT, and math.RA
Abstract: We give a new construction of a C*-algebra from a cancellative semigroup $P$ via partial isometric representations, generalising the construction from the second named author's thesis. We then study our construction in detail for the special case when $P$ is an LCM semigroup. In this case we realize our algebras as inverse semigroup algebras and groupoid algebras, and apply our construction to free semigroups and Zappa-Sz\'ep products associated to self-similar groups.