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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Klimek, Slawomir¹  McBride, Matt² 

[1] Indiana Univ Purdue Univ, Dept Math Sci, 402 N Blackford St, Indianapolis, IN 46202 USA

[2] Mississippi State Univ, Dept Math & Stat, 175 Presidents Cir, Mississippi State, MS 39762 USA

关键词: Noncommutative geometry;    Dirac operators;    APS boundary conditions;    Noncommutative tori;   

DOI  :  10.1016/j.jmaa.2019.123690

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free