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This article is cited in 8 scientific papers (total in 8 papers)
Equivariant Join and Fusion of Noncommutative Algebras
Ludwik Dąbrowskia, Tom Hadfieldb, Piotr M. Hajacc a SISSA (Scuola Internazionale Superiore di Studi Avanzati),
Via Bonomea 265, 34136 Trieste, Italy
b G-Research, Whittington House, 19-30 Alfred Place, London WC1E 7EA, UK
c Instytut Matematyczny, Polska Akademia Nauk, ul.Śniadeckich 8, 00-656 Warszawa, Poland
Abstract:
We translate the concept of the join of topological spaces to the language of $C^*$-algebras, replace the $C^*$-algebra of functions on the interval $[0,1]$ with evaluation maps at $0$ and $1$ by a unital $C^*$-algebra $C$ with appropriate two surjections, and introduce the notion of the fusion of unital $C^*$-algebras. An appropriate modification of this construction yields the fusion comodule algebra of a comodule algebra $P$ with the coacting Hopf algebra $H$. We prove that, if the comodule algebra $P$ is principal, then so is the fusion comodule algebra. When $C=C([0,1])$ and the two surjections are evaluation maps at $0$ and $1$, this result is a noncommutative-algebraic incarnation of the fact that, for a compact Hausdorff principal $G$-bundle $X$, the diagonal action of $G$ on the join $X*G$ is free.
Keywords:
$C^*$-algebras; Hopf algebras; free actions.
Received: June 30, 2015; in final form October 3, 2015; Published online October 13, 2015
Citation:
Ludwik Dąbrowski, Tom Hadfield, Piotr M. Hajac, “Equivariant Join and Fusion of Noncommutative Algebras”, SIGMA, 11 (2015), 082, 7 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1063 https://www.mathnet.ru/eng/sigma/v11/p82
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