Piecewise Principal Coactions of Co-Commutative Hopf Algebras
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Piecewise Principal Coactions of Co-Commutative Hopf Algebras
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| Creator |
Zieliński, B.
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| 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.
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| Date |
2019-02-10T10:02:30Z
2019-02-10T10:02:30Z 2014 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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