Abstract
In this paper, we consider the [Formula: see text]-algebra generated by finitely many annihilation operators acting on the weakly monotone Fock space, and we call it weakly monotone [Formula: see text]-algebra. We give an abstract presentation for this algebra, showing that it is isomorphic to a suitable quotient of a Cuntz–Krieger [Formula: see text]-algebra 𝒪A corresponding to a suitable matrix [Formula: see text]. Furthermore, we show that the diagonal subalgebra of the weakly monotone [Formula: see text]-algebra is a MASA and we give a detailed description of its Gelfand spectrum.
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