Hajac, P. M., Krähmer, U., Matthea, R. and Zielinski, B. (2011) Piecewise principal comodule algebras. Journal of Noncommutative Geometry, 5(4), pp. 591-614. (doi: 10.4171/JNCG/88)
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118893.pdf - Accepted Version 378kB |
Abstract
A comodule algebra P over a Hopf algebra H with bijective antipode is called principal if the coaction of H is Galois and P is H-equivariantly projective (faithfully flat) over the coaction-invariant subalgebra PcoH. We prove that principality is a piecewise property: given N comodule-algebra surjections P → P_i whose kernels intersect to zero, P is principal if and only if all P_i’s are principal. Furthermore, assuming the principality of P, we show that the lattice these kernels generate is distributive if and only if so is the lattice obtained by intersection with PcoH. Finally, assuming the above distributivity property, we obtain a flabby sheaf of principal comodule algebras over a certain space that is universal for all such N-families of surjections P → P_i and such that the comodule algebra of global sections is P.
| Item Type: | Articles |
|---|---|
| Additional Information: | This work was partially supported by the European Commission grants EIF-515144(UK), MKTD-CT-2004-509794 (RM), the Polish Government grants 1 P03A 036 26 (PMH, RM), 115/E-343/SPB/6.PR UE/DIE 50/2005-2008 (PMH, BZ), and the University of L´od´z Grant 795 (BZ). |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Kraehmer, Dr Ulrich |
| Authors: | Hajac, P. M., Krähmer, U., Matthea, R., and Zielinski, B. |
| Subjects: | Q Science > QA Mathematics |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics |
| Research Group: | Algebra |
| Journal Name: | Journal of Noncommutative Geometry |
| Journal Abbr.: | J. Noncommut. Geom. |
| Publisher: | European Mathematical Society |
| ISSN: | 1661-6952 |
| ISSN (Online): | 1661-6960 |
| Copyright Holders: | Copyright © 2011 European Mathematical Society |
| First Published: | First published in Journal of Noncommutative Geometry 5(4): 591-614 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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