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Weakly-monotone C*-algebras as Exel-Laca algebras (2402.08435v3)
Published 13 Feb 2024 in math.OA
Abstract: An abstract characterization of weakly monotone $C*$-algebras, namely the concrete $C*$-algebras generated by creators and annihilators acting on the so-called weakly monotone Fock spaces, is given in terms of (quotient of) suitable Exel-Laca algebras. The weakly monotone $C*$-algebra indexed by $\mathbb{N}$ is shown to be a type-I $C*$-algebra and its representation theory is entirely determined, whereas the weakly monotone $C*$-algebra indexed by $\mathbb{Z}$ is shown not to be of type $I$.