On the “quantum disk” and a “non-commutative circle”

Gabriel Nagy () and Alexandru Nica ()
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Gabriel Nagy: Kansas State University, Department of Mathematics
Alexandru Nica: University of California, Department of Mathematics

A chapter in Algebraic Methods in Operator Theory, 1994, pp 276-290 from Springer

Abstract: Abstract Let T q be the universal C*-aIgebra generated by an element zsatisfying the equation: $$z{{z}^{*}} = q{{z}^{*}} + \left( {1 - q} \right)I$$ where q ∈ [-1, 1] is a parameter. We show that, in contrast to T q for -1 0, $$\phi - 1$$ is the restriction to T q of the Haar measure on the quantum group S √q U(2). The distribution (with respect to $${{\phi }_{q}}$$ of the real part of the generator z is deformed from the semicircle law $$\frac{2}{\pi }\sqrt {{1 - {{t}^{2}}dt}}$$ , at q = 0, to |t|dt, at q = -1.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0255-4_27

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DOI: 10.1007/978-1-4612-0255-4_27

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