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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147156 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862531074021654528 |
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| author | Dąbrowski, L. Hadfield, T. Hajac, P.M. |
| author_facet | Dąbrowski, L. Hadfield, T. Hajac, P.M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-24T04:38:52Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147156 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:38:52Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Dąbrowski, L. Hadfield, T. Hajac, P.M. 2019-02-13T17:50:17Z 2019-02-13T17:50:17Z 2015 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 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Equivariant Join and Fusion of Noncommutative Algebras Article published earlier |
| spellingShingle | Equivariant Join and Fusion of Noncommutative Algebras Dąbrowski, L. Hadfield, T. Hajac, P.M. |
| title | 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_short | Equivariant Join and Fusion of Noncommutative Algebras |
| title_sort | equivariant join and fusion of noncommutative algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147156 |
| work_keys_str_mv | AT dabrowskil equivariantjoinandfusionofnoncommutativealgebras AT hadfieldt equivariantjoinandfusionofnoncommutativealgebras AT hajacpm equivariantjoinandfusionofnoncommutativealgebras |