518 research outputs found
Rationally Isomorphic Hermitian Forms and Torsors of Some Non-Reductive Groups
Let be a semilocal Dedekind domain. Under certain assumptions, we show
that two (not necessarily unimodular) hermitian forms over an -algebra with
involution, which are rationally ismorphic and have isomorphic semisimple
coradicals, are in fact isomorphic. The same result is also obtained for
quadratic forms equipped with an action of a finite group. The results have
cohomological restatements that resemble the Grothendieck--Serre conjecture,
except the group schemes involved are not reductive. We show that these group
schemes are closely related to group schemes arising in Bruhat--Tits theory.Comment: 27 pages. Changes from previous version: Section 5 was split into two
sections, several proofs have been simplified, other mild modification
Signatures of hermitian forms and the Knebusch Trace Formula
Signatures of quadratic forms have been generalized to hermitian forms over
algebras with involution. In the literature this is done via Morita theory,
which causes sign ambiguities in certain cases. In this paper, a hermitian
version of the Knebusch Trace Formula is established and used as a main tool to
resolve these ambiguities.
The last page is an erratum for the published version. We inadvertently (I)
gave an incorrect definition of adjoint involutions; (II) omitted dealing with
the case . As , the
omission does not affect our reasoning or our results. For the sake of
completeness we point out where some small changes should be made in the
published version.Comment: This is the final version before publication. The last page is an
updated erratum for the published versio
Division, adjoints, and dualities of bilinear maps
The distributive property can be studied through bilinear maps and various
morphisms between these maps. The adjoint-morphisms between bilinear maps
establish a complete abelian category with projectives and admits a duality.
Thus the adjoint category is not a module category but nevertheless it is
suitably familiar. The universal properties have geometric perspectives. For
example, products are orthogonal sums. The bilinear division maps are the
simple bimaps with respect to nondegenerate adjoint-morphisms. That formalizes
the understanding that the atoms of linear geometries are algebraic objects
with no zero-divisors. Adjoint-isomorphism coincides with principal isotopism;
hence, nonassociative division rings can be studied within this framework.
This also corrects an error in an earlier pre-print; see Remark 2.11
Pfister involutions
The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras with involution are studied. It is proven that, up to degree 16, over any extension over which the algebra splits, the involution is adjoint to a Pfister form. Moreover, cohomological invariants of those algebras with involution are discusse
Algebraic lattice constellations: bounds on performance
In this work, we give a bound on performance of any full-diversity lattice constellation constructed from algebraic number fields. We show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a negligible coding gain. Furthermore, we discuss constructions, minimum product distance, and bounds for full-diversity complex rotated Z[i]/sup n/-lattices for any dimension n, which avoid the need of component interleaving
On the Grothendieck-Serre Conjecture for Classical Groups
We prove some new cases of the Grothendieck-Serre conjecture for classical
groups. This is based on a new construction of the Gersten-Witt complex for
Witt groups of Azumaya algebras with involution on regular semilocal rings,
with explicit second residue maps; the complex is shown to be exact when the
ring is of dimension (or , with additional hypotheses on the
algebra with involution). Note that we do not assume that the ring contains a
field.Comment: 37 pages. Changes from previous version include many improvements to
section 2. Comments are welcom
An Improved Model for Relativistic Solar Proton Acceleration applied to the 2005 January 20 and Earlier Events
This paper presents results on modelling the ground level response of the
higher energy protons for the 2005 January 20 ground level enhancement (GLE).
This event, known as GLE 69, produced the highest intensity of relativistic
solar particles since the famous event on 1956 February 23. The location of
recent X-ray and gamma-ray emission (N14 W61) was near to Sun-Earth connecting
magnetic field lines, thus providing the opportunity to directly observe the
acceleration source from Earth. We restrict our analysis to protons of energy
greater than 450 MeV to avoid complications arising from transport processes
that can affect the propagation of low energy protons. In light of this revised
approach we have reinvestigated two previous GLEs: those of 2000 July 14 (GLE
59) and 2001 April 15 (GLE 60). Within the limitations of the spectral forms
employed, we find that from the peak (06:55 UT) to the decline (07:30 UT)
phases of GLE 69, neutron monitor observations from 450 MeV to 10 GeV are best
fitted by the Gallegos-Cruz & Perez-Peraza stochastic acceleration model. In
contrast, the Ellison & Ramaty spectra did not fit the neutron monitor
observations as well. This result suggests that for GLE 69, a stochastic
process cannot be discounted as a mechanism for relativistic particle
acceleration, particularly during the initial stages of this solar event. For
GLE 59 we find evidence that more than one acceleration mechanism was present,
consistent with both shock and stochastic acceleration processes dominating at
different times of the event. For GLE 60 we find that Ellison & Ramaty spectra
better represent the neutron monitor observations compared to stochastic
acceleration spectra. The results for GLEs 59 and 60 are in agreement with our
previous work.Comment: 42 pages, 10 figures, 10 tables, published in ApJ, August 200
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