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Media type:
E-Article
Title:
The pullbacks of principal coactions
Contributor:
Hajac, Piotr M.;
Wagner, Elmar
Published:
European Mathematical Society - EMS - Publishing House GmbH, 2014
Published in:
Documenta Mathematica, 19 (2014), Seite 1025-1060
Language:
Not determined
DOI:
10.4171/dm/473
ISSN:
1431-0635;
1431-0643
Origination:
Footnote:
Description:
We prove that the class of principal coactions is closed under one-surjective pullbacks in an appropriate category of algebras equipped with left and right coactions. This allows us to handle cases of C^* -algebras lacking two different non-trivial ideals. It also allows us to go beyond the category of comodule algebras. As an example of the former, we carry out an index computation for noncommutative line bundles over the standard Podle´s sphere using the Mayer-Vietoris-type arguments afforded by a one-surjective pullback presentation of the C^* -algebra of this quantum sphere. To instantiate the latter, we define a family of coalgebraic noncommutative deformations of the \mathrm{U}(1) -principal bundle \mathrm{S}^7\rightarrow{C}\mathrm{P}^3 .