1,616 research outputs found
Quillen-Suslin theory for a structure theorem for the Elementary Symplectic Group
A new set of elementary symplectic elements is described, It is shown that
these also generate the elementary symplectic group {\rm ESp}. These
generators are more symmetrical than the usual ones, and are useful to study
the action of the elementary symplectic group on unimodular rows. Also, an
alternate proof of, {\rm ESp} is a normal subgroup of {\rm
Sp}, is shown using the Local Global Principle of D. Quillen for the
new set of generators.Comment: 14 pages, few typos corrected. To appear in Ramanujan Math. Soc.
Lect. Notes Se
Local-Global Principle for Transvection Groups
In this article we extend the validity Suslin's Local-Global Principle for
the elementary transvection subgroup of the general linear group, the
symplectic group, and the orthogonal group, where n > 2, to a Local-Global
Principle for the elementary transvection subgroup of the automorphism group
Aut(P) of either a projective module P of global rank > 0 and constant local
rank > 2, or of a nonsingular symplectic or orthogonal module P of global
hyperbolic rank > 0 and constant local hyperbolic rank > 2. In Suslin's
results, the local and global ranks are the same, because he is concerned only
with free modules. Our assumption that the global (hyperbolic) rank > 0 is used
to define the elementary transvection subgroups. We show further that the
elementary transvection subgroup ET(P) is normal in Aut(P), that ET(P) = T(P)
where the latter denotes the full transvection subgroup of Aut(P), and that the
unstable K_1-group K_1(Aut(P)) = Aut(P)/ET(P) = Aut(P)/T(P) is nilpotent by
abelian, provided R has finite stable dimension. The last result extends
previous ones of Bak and Hazrat for the above mentioned classical groups.
An important application to the results in the current paper can be found in
the work of last two named authors where they have studied the decrease in the
injective stabilization of classical modules over a non-singular affine algebra
over perfect C_1-fields. We refer the reader to that article for more details.Comment: 15 page
GMOSS: All-sky model of spectral radio brightness based on physical components and associated radiative processes
We present Global MOdel for the radio Sky Spectrum (GMOSS) -- a novel,
physically motivated model of the low-frequency radio sky from 22 MHz to 23
GHz. GMOSS invokes different physical components and associated radiative
processes to describe the sky spectrum over 3072 pixels of
resolution. The spectra are allowed to be convex, concave or of more complex
form with contributions from synchrotron emission, thermal emission and
free-free absorption included. Physical parameters that describe the model are
optimized to best fit four all-sky maps at 150 MHz, 408 MHz, 1420 MHz and 23
GHz and two maps at 22 MHz and 45 MHz generated using the Global Sky Model of
de Oliveira-Costa et al. (2008). The fractional deviation of model to data has
a median value of and is less than for of the pixels.
Though aimed at modeling of foregrounds for the global signal arising from the
redshifted 21-cm line of Hydrogen during Cosmic Dawn and Epoch of Reionization
(EoR) - over redshifts , GMOSS is well suited for any
application that requires simulating spectra of the low-frequency radio sky as
would be observed by the beam of any instrument. The complexity in spectral
structure that naturally arises from the underlying physics of the model
provides a useful expectation for departures from smoothness in EoR foreground
spectra and hence may guide the development of algorithms for EoR signal
detection. This aspect is further explored in a subsequent paper.Comment: 19 pages, 7 figure
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