Dirac type operators on the quantum solid torus with global boundary conditions

2016/11/04 by Klimek, Slawomir, McBride, Matt
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1611.01556

Abstract

We define a noncommutative space we call the quantum solid torus. It is an example of a noncommutative manifold with a noncommutative boundary. We study quantum Dirac type operators subject to Atiyah-Patodi-Singer like boundary conditions on the quantum solid torus. We show that such operators have compact inverse, which means that the corresponding boundary value problem is elliptic.

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