Equivariant Join and Fusion of Noncommutative Algebras
Open Access
- 13 October 2015
- journal article
- research article
- Published by SIGMA (Symmetry, Integrability and Geometry: Methods and Application) in Symmetry, Integrability and Geometry: Methods and Applications
- Vol. 11, 082
- https://doi.org/10.3842/sigma.2015.082
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
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This publication has 1 reference indexed in Scilit:
- Piecewise principal comodule algebrasJournal of Noncommutative Geometry, 2011