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Equivariant Join and Fusion of Noncommutative Algebras
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Equivariant Join and Fusion of Noncommutative Algebras
Інший ID:
2010 Mathematics Subject Classification: 46L85; 58B32
DOI:10.3842/SIGMA.2015.082
DOI:10.3842/SIGMA.2015.082
Посилання:
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.
Підтримка:
All authors are grateful to Piotr M. So ltan and Karen R. Strung for references concerning the
minimal tensor product and the Jiang–Su C
∗
-algebra respectively. Ludwik D¸abrowski and Piotr
M. Hajac were partially supported by PRIN 2010-11 grant “Operator Algebras, Noncommutative
Geometry and Applications” and NCN grant 2011/01/B/ST1/06474, respectively. Tom Hadfield
was financed via the EU Transfer of Knowledge contract MKTD-CT-2004-509794. Also, Piotr
M. Hajac is very thankful to SISSA for its hospitality.
Дата:
2015
Переглядів:
566
Завантажень:
236
Анотація:
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.
