Crossed Module Actions on Continuous Trace C*-Algebras

2015/06/30 by Ralf Meyer, Ulrich Pennig
Mathematics · #Action (physics) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Computer science #Equivariant map #Extension (predicate logic) #Geometry #Lift (data mining) #Mathematics #Physics #Pure mathematics #Quantum mechanics #Spectrum (functional analysis) #TRACE (psycholinguistics) #Torus #math.FA #math.OA #msc:46L60 #msc:58B34

paper · pdf · doi:10.1007/s00220-016-2638-3

published as Comm. Math. Phys. 346, p. 115-142 (2016) · 27 pages, added background material about T-Duality, added references, extended section about non-associative C*-algebras

arxiv created 2016/03/03 · openalex publication_date 2016/05/20 · arxiv updated 2017/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We lift an action of a torus \mathbbTⁿ on the spectrum of a continuous trace algebra to an action of a certain crossed module of Lie groups that is an extension of ℝⁿ. We compute equivariant Brauer and Picard groups for this crossed module and describe the obstruction to the existence of an action of ℝⁿ in our framework.

Citations

• Introduction to bicategories
• T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology
• Topology and Flux of T-Dual Manifolds with Circle Actions
• T-Duality: Topology Change from H-Flux