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Crossed products of C*-algebras for singular actions

Grundling H, Neeb KH (2014)

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Publication Type: Journal article, Original article

Publication year: 2014

Journal

Publisher: Elsevier

Book Volume: 266

Pages Range: 5199 - 5269

Journal Issue: 8

DOI: 10.1016/j.jfa.2014.01.022

Abstract

We consider group actions α:G→Aut(A)$\alpha :G\to \mathrm{Aut}(\mathcal{A})$ of topological groups G   on C^⁎$C^{⁎}$-algebras A$\mathcal{A}$ of the type which occurs in many physics models. These are singular actions in the sense that they need not be strongly continuous, or the group need not be locally compact. We develop a “crossed product host” in analogy to the usual crossed product for strongly continuous actions of locally compact groups, in the sense that its representation theory is in a natural bijection with the covariant representation theory of the action α:G→Aut(A)$\alpha :G\to \mathrm{Aut}(\mathcal{A})$. We prove a uniqueness theorem for crossed product hosts, and analyze existence conditions. We also present a number of examples where a crossed product host exists, but the usual crossed product does not. For actions where a crossed product host does not exist, we obtain a “maximal” invariant subalgebra for which a crossed product host exists. We further study the case of a discontinuous action α:G→Aut(A)$\alpha :G\to \mathrm{Aut}(\mathcal{A})$ of a locally compact group in detail.

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How to cite

APA:

Grundling, H., & Neeb, K.H. (2014). Crossed products of C*-algebras for singular actions. Journal of Functional Analysis, 266(8), 5199 - 5269. https://dx.doi.org/10.1016/j.jfa.2014.01.022

MLA:

Grundling, Hendrik, and Karl Hermann Neeb. "Crossed products of C*-algebras for singular actions." Journal of Functional Analysis 266.8 (2014): 5199 - 5269.

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