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arXiv · 1506.01311

Crossed module actions on continuous trace $C^*$-algebras

Ralf Meyer·Ulrich Pennig
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Abstract

We lift an action of a torus $\mathbb{T}^n$ on the spectrum of a continuous trace algebra to an action of a certain crossed module of Lie groups that is an extension of $\mathbb{R}^n$. We compute equivariant Brauer and Picard groups for this crossed module and describe the obstruction to the existence of an action of $\mathbb{R}^n$ in our framework.

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Ralf Meyer, Ulrich Pennig. 2015-06-03. Crossed module actions on continuous trace $C^*$-algebras. https://doi.org/10.1007/s00220-016-2638-3

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