Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 012, 22 pages      arXiv:1410.0733

The Quantum Pair of Pants

Slawomir Klimek a, Matt Mcbride b, Sumedha Rathnayake a and Kaoru Sakai a
a) 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

Received October 24, 2014, in final form February 03, 2015; Published online February 10, 2015

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.

Key words: quantum domains; $C^*$-algebras.

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