Finitely generated weakly monotone C*-algebra

In this paper, 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 presentation for this algebra, showing that it is isomorphic to a suitable quotient of a Cuntz–Krieger C*-algebra 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 a detailed description of its Gelfand spectrum.