Piecewise Principal Coactions of Co-Commutative Hopf Algebras
Principal comodule algebras can be thought of as objects representing principal bundles in non-commutative geometry. A crucial component of a principal comodule algebra is a strong connection map. For some applications it suffices to prove that such a map exists, but for others, such as computing th...
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| Date: | 2014 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/146612 |
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| Cite this: | Piecewise Principal Coactions of Co-Commutative Hopf Algebras / B. Zieliński // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 23 назв. — англ. |
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irk-123456789-1466122019-02-11T01:23:12Z Piecewise Principal Coactions of Co-Commutative Hopf Algebras Zieliński, B. Principal comodule algebras can be thought of as objects representing principal bundles in non-commutative geometry. A crucial component of a principal comodule algebra is a strong connection map. For some applications it suffices to prove that such a map exists, but for others, such as computing the associated bundle projectors or Chern-Galois characters, an explicit formula for a strong connection is necessary. It has been known for some time how to construct a strong connection map on a multi-pullback comodule algebra from strong connections on multi-pullback components, but the known explicit general formula is unwieldy. In this paper we derive a much easier to use strong connection formula, which is not, however, completely general, but is applicable only in the case when a Hopf algebra is co-commutative. Because certain linear splittings of projections in multi-pullback comodule algebras play a crucial role in our construction, we also devote a significant part of the paper to the problem of existence and explicit formulas for such splittings. Finally, we show example application of our work. 2014 Article Piecewise Principal Coactions of Co-Commutative Hopf Algebras / B. Zieliński // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 23 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58B32; 16T05 DOI:10.3842/SIGMA.2014.088 http://dspace.nbuv.gov.ua/handle/123456789/146612 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
Principal comodule algebras can be thought of as objects representing principal bundles in non-commutative geometry. A crucial component of a principal comodule algebra is a strong connection map. For some applications it suffices to prove that such a map exists, but for others, such as computing the associated bundle projectors or Chern-Galois characters, an explicit formula for a strong connection is necessary. It has been known for some time how to construct a strong connection map on a multi-pullback comodule algebra from strong connections on multi-pullback components, but the known explicit general formula is unwieldy. In this paper we derive a much easier to use strong connection formula, which is not, however, completely general, but is applicable only in the case when a Hopf algebra is co-commutative. Because certain linear splittings of projections in multi-pullback comodule algebras play a crucial role in our construction, we also devote a significant part of the paper to the problem of existence and explicit formulas for such splittings. Finally, we show example application of our work. |
| format |
Article |
| author |
Zieliński, B. |
| spellingShingle |
Zieliński, B. Piecewise Principal Coactions of Co-Commutative Hopf Algebras Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Zieliński, B. |
| author_sort |
Zieliński, B. |
| title |
Piecewise Principal Coactions of Co-Commutative Hopf Algebras |
| title_short |
Piecewise Principal Coactions of Co-Commutative Hopf Algebras |
| title_full |
Piecewise Principal Coactions of Co-Commutative Hopf Algebras |
| title_fullStr |
Piecewise Principal Coactions of Co-Commutative Hopf Algebras |
| title_full_unstemmed |
Piecewise Principal Coactions of Co-Commutative Hopf Algebras |
| title_sort |
piecewise principal coactions of co-commutative hopf algebras |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146612 |
| citation_txt |
Piecewise Principal Coactions of Co-Commutative Hopf Algebras / B. Zieliński // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 23 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT zielinskib piecewiseprincipalcoactionsofcocommutativehopfalgebras |
| first_indexed |
2025-07-11T00:19:40Z |
| last_indexed |
2025-07-11T00:19:40Z |
| _version_ |
1837307716723277824 |