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...
Saved in:
| Date: | 2015 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2015
|
| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
|---|