Equivariant Join and Fusion of Noncommutative Algebras

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...

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Datum:2015
Hauptverfasser: Dąbrowski, L., Hadfield, T., Hajac, P.M.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2015
Schriftenreihe:Symmetry, Integrability and Geometry: Methods and Applications
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Equivariant Join and Fusion of Noncommutative Algebras / L. Dąbrowski, T. Hadfield, P.M. Hajac // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 13 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung: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.