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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| Date: | 2015 |
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| Language: | English |
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Інститут математики НАН України
2015
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| 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. |
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oai:nasplib.isofts.kiev.ua:123456789-1471562025-02-23T17:37:24Z Equivariant Join and Fusion of Noncommutative Algebras Dąbrowski, L. Hadfield, T. Hajac, P.M. 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. 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. 2015 Article 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. 1815-0659 2010 Mathematics Subject Classification: 46L85; 58B32 DOI:10.3842/SIGMA.2015.082 https://nasplib.isofts.kiev.ua/handle/123456789/147156 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| language |
English |
| description |
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. |
| format |
Article |
| author |
Dąbrowski, L. Hadfield, T. Hajac, P.M. |
| spellingShingle |
Dąbrowski, L. Hadfield, T. Hajac, P.M. Equivariant Join and Fusion of Noncommutative Algebras Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Dąbrowski, L. Hadfield, T. Hajac, P.M. |
| author_sort |
Dąbrowski, L. |
| title |
Equivariant Join and Fusion of Noncommutative Algebras |
| title_short |
Equivariant Join and Fusion of Noncommutative Algebras |
| title_full |
Equivariant Join and Fusion of Noncommutative Algebras |
| title_fullStr |
Equivariant Join and Fusion of Noncommutative Algebras |
| title_full_unstemmed |
Equivariant Join and Fusion of Noncommutative Algebras |
| title_sort |
equivariant join and fusion of noncommutative algebras |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT dabrowskil equivariantjoinandfusionofnoncommutativealgebras AT hadfieldt equivariantjoinandfusionofnoncommutativealgebras AT hajacpm equivariantjoinandfusionofnoncommutativealgebras |
| first_indexed |
2025-07-22T04:24:17Z |
| last_indexed |
2025-07-22T04:24:17Z |
| _version_ |
1838319673645465600 |