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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2015 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147156 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147156 |
|---|---|
| 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Equivariant Join and Fusion of Noncommutative Algebras |
| spellingShingle |
Equivariant Join and Fusion of Noncommutative Algebras Dąbrowski, L. Hadfield, T. Hajac, P.M. |
| 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 |
| author |
Dąbrowski, L. Hadfield, T. Hajac, P.M. |
| author_facet |
Dąbrowski, L. Hadfield, T. Hajac, P.M. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147156 |
| fulltext |
|
| 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. |
| work_keys_str_mv |
AT dabrowskil equivariantjoinandfusionofnoncommutativealgebras AT hadfieldt equivariantjoinandfusionofnoncommutativealgebras AT hajacpm equivariantjoinandfusionofnoncommutativealgebras |
| first_indexed |
2025-11-24T04:38:52Z |
| last_indexed |
2025-11-24T04:38:52Z |
| _version_ |
1850840830407868416 |