This article is cited in 3 papers

The Quantum Pair of Pants

Slawomir Klimek^a, Matt McBride^b, Sumedha Rathnayake^a, Kaoru Sakai<sup>a

a</sup> Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN 46202, USA
^b Department of Mathematics, University of Oklahoma, 601 Elm St., Norman, OK 73019, USA

Abstract: We compute the spectrum of the operator of multiplication by the complex coordinate in a Hilbert space of holomorphic functions on a disk with two circular holes. Additionally we determine the structure of the $C^*$-algebra generated by that operator. The algebra can be considered as the quantum pair of pants.

Keywords: quantum domains; $C^*$-algebras.

MSC: 46L35

Received: October 24, 2014; in final form February 3, 2015; Published online February 10, 2015

Language: English

DOI: 10.3842/SIGMA.2015.012

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ArXiv: 1410.0733