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Finitely generated weakly monotone C*-algebra (2402.19081v2)
Published 29 Feb 2024 in math.OA
Abstract: We consider the $C*$-algebra generated by finitely many annihilation operators acting on the weakly monotone Fock space, and we call it weakly monotone $C*$-algebra. We give an abstract representation for this algebra, showing that it is isomorphic to a suitable quotient of a Cuntz-Krieger $C*$-algebra $\mathcal{O}_A$ corresponding to a suitable matrix $A$. Furthermore, we show that the diagonal subalgebra of the weakly monotone $C*$-algebra is a MASA and we give the detailed description of its Gelfand spectrum.