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Piecewise principal comodule algebras | | Piotr M. Hajac
; Ulrich Kraehmer
; Rainer Matthes
; Bartosz Zielinski
; | | Date: |
10 Jul 2007 | | 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 $P^{co H}$. We prove
that principality is a piecewise property: given N comodule-algebra surjections
$P o P_i$ 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 $P^{co H}$. Finally, assuming the
above distributivity property, we obtain a flabby sheaf $mathcal P$ of
principal comodule algebras over a certain space universal for all such
N-families of surjections $P o P_i$ and such that $mathcal P$ of this space
is the comodule algebra P. | | Source: | arXiv, arxiv.0707.1344 | | Services: | Forum | Review | PDF | Favorites | |
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