370 research outputs found
Hopf modules, Frobenius functors and (one-sided) Hopf algebras
We investigate the property of being Frobenius for some functors strictly
related with Hopf modules over a bialgebra and how this property reflects on
the latter. In particular, we characterize one-sided Hopf algebras with
anti-(co)multiplicative one-sided antipode as those for which the free Hopf
module functor is Frobenius. As a by-product, this leads us to relate the
property of being an FH-algebra (in the sense of Pareigis) for a given
bialgebra with the property of being Frobenius for certain naturally associated
functors.Comment: 20 pages. Major changes: considerably shortened. Comments are welcom
Globalization for geometric partial comodules
We discuss globalization for geometric partial comodules in a monoidal
category with pushouts and we provide a concrete procedure to construct it,
whenever it exists. The mild assumptions required by our approach make it
possible to apply it in a number of contexts of interests, recovering and
extending numerous ad hoc globalization constructions from the literature in
some cases and providing obstruction for globalization in some other cases.Comment: 18 pages. Major revision. Results and global presentation improved.
Comments are welcome
Topological tensor product of bimodules, complete Hopf Algebroids and convolution algebras
Given a finitely generated and projective Lie-Rinehart algebra, we show that
there is a continuous homomorphism of complete commutative Hopf algebroids
between the completion of the finite dual of its universal enveloping Hopf
algebroid and the associated convolution algebra. The topological Hopf
algebroid structure of this convolution algebra is here clarified, by providing
an explicit description of its topological antipode as well as of its other
structure maps. Conditions under which that homomorphism becomes an
homeomorphism are also discussed. These results, in particular, apply to the
smooth global sections of any Lie algebroid over a smooth (connected) manifold
and they lead a new formal groupoid scheme to enter into the picture. In the
Appendix we develop the necessary machinery behind complete Hopf algebroid
constructions, which involves also the topological tensor product of filtered
bimodules over filtered rings.Comment: Minor changes, 33 pages. To appear in CC
A Catalogue of Galaxies in the HDF-South: Photometry and Structural Parameters
We describe the construction of a catalogue of galaxies in the optical field
of the Hubble Deep Field South. The HDF-S observations produced WFPC2 images in
U, B, V, and I, the version 1 data have been made public on 23 November 1999.
The effective field of view is 4.38 arcmin, and the 5 limiting
magnitudes (in a FWHM aperture) are 28.87, 29.71, 30.19, 29.58 in the U, B, V
and I bands, respectively. We created a catalogue for each pass-band
(I, V, B, U), using simulations to account for
incompleteness and spurious sources contamination. Along with photometry in all
bands, we determined on the I-selected catalogue (I)
structural parameters, such as a metric apparent size, derived from the
petrosian radius, an asymmetry index, light concentration indexes and the mean
surface brightness within the petrosian radius.Comment: 10 pages, 11 figures. Accepted for publication in A&ASS. The catalog
is available in the source and at
http://www.merate.mi.astro.it/~saracco/science.htm
-deformations of graded rings
We prove in a very general framework several versions of the classical
Poincar\'e-Birkhoff-Witt Theorem, which extend results from [BeGi, BrGa, CS,
HvOZ, WW]. Applications and examples are discussed in the last part of the
paper
On anchored Lie algebras and the Connes-Moscovici's bialgebroid construction
We show how the Connes-Moscovici's bialgebroid construction naturally
provides universal objects for Lie algebras acting on non-commutative algebras.Comment: 35 pages. Comments are welcome
On anchored Lie algebras and the Connes–Moscovici bialgebroid construction
We show how the Connes–Moscovici bialgebroid construction naturally provides universal objects for Lie algebras acting on non-commutative algebras. As a supplement, we see how these objects interact with the study of flat bimodule connections.info:eu-repo/semantics/publishe
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