Geodesic
The pullbacks of principal coactions
Documenta mathematica, Tome 19 (2014), pp. 1025-1060.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\mathrm{S}^7\rightarrow\{C}\mathrm{P}^3$.
Classification : 46L85, 58B32
Keywords: coalgebra-Galois extension, entwining structure, equivariant projectivity, strong connection, Hopf algebra, quantum group, index pairing 
@article{DOCMA_2014__19__a10,
     author = {Hajac, Piotr M. and Wagner, Elmar},
     title = {The pullbacks of principal coactions},
     journal = {Documenta mathematica},
     pages = {1025--1060},
     publisher = {mathdoc},
     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a10/}
}
TY  - JOUR
AU  - Hajac, Piotr M.
AU  - Wagner, Elmar
TI  - The pullbacks of principal coactions
JO  - Documenta mathematica
PY  - 2014
SP  - 1025
EP  - 1060
VL  - 19
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a10/
LA  - en
ID  - DOCMA_2014__19__a10
ER  - 
%0 Journal Article
%A Hajac, Piotr M.
%A Wagner, Elmar
%T The pullbacks of principal coactions
%J Documenta mathematica
%D 2014
%P 1025-1060
%V 19
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a10/
%G en
%F DOCMA_2014__19__a10
Hajac, Piotr M.; Wagner, Elmar. The pullbacks of principal coactions. Documenta mathematica, Tome 19 (2014), pp. 1025-1060. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a10/