Exotic group C*-algebras in noncommutative duality

S. Kaliszewski; Magnus B. Landstad; John Quigg

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arXiv · 1211.4982

Exotic group C*-algebras in noncommutative duality

S. Kaliszewski·Magnus B. Landstad·John Quigg

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Abstract

We show that for a locally compact group G there is a one-to-one correspondence between G-invariant weak*-closed subspaces E of the Fourier-Stieltjes algebra B(G) containing B_r(G) and quotients C*_E(G) of C*(G) which are intermediate between C*(G) and the reduced group algebra C*_r(G). We show that the canonical comultiplication on C*(G) descends to a coaction or a comultiplication on C*_E(G) if and only if E is an ideal or subalgebra, respectively. When αis an action of G on a C*-algebra B, we define "E-crossed products" B\rtimes_{α,E} G lying between the full crossed product and the reduced one, and we conjecture that these "intermediate crossed products" satisfy an "exotic" version of crossed-product duality involving C*_E(G).

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S. Kaliszewski, Magnus B. Landstad, John Quigg. 2013-08-30. Exotic group C*-algebras in noncommutative duality. https://arxiv.org/abs/1211.4982

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