Piecewise principal comodule algebras

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)

118893.pdf - Accepted Version



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).
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 (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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