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arXiv · 2402.19081

Finitely generated weakly monotone C*-algebra

Maria Elena Griseta·Janusz Wysoczański
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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.

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Maria Elena Griseta, Janusz Wysoczański. 2024-02-29. Finitely generated weakly monotone C*-algebra. https://arxiv.org/abs/2402.19081

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