382 research outputs found
Graded contractions of bilinear invariant forms of Lie algebras
We introduce a new construction of bilinear invariant forms on Lie algebras,
based on the method of graded contractions. The general method is described and
the -, -, and -contractions are
found. The results can be applied to all Lie algebras and superalgebras (finite
or infinite dimensional) which admit the chosen gradings. We consider some
examples: contractions of the Killing form, toroidal contractions of ,
and we briefly discuss the limit to new WZW actions.Comment: 15 page
Graded Contractions of Affine Kac-Moody Algebras
The method of graded contractions, based on the preservation of the
automorphisms of finite order, is applied to the affine Kac-Moody algebras and
their representations, to yield a new class of infinite dimensional Lie
algebras and representations. After the introduction of the horizontal and
vertical gradings, and the algorithm to find the horizontal toroidal gradings,
I discuss some general properties of the graded contractions, and compare them
with the In\"on\"u-Wigner contractions. The example of is discussed
in detail.Comment: 23 pages, Ams-Te
Wormholes, Gamma Ray Bursts and the Amount of Negative Mass in the Universe
In this essay, we assume that negative mass objects can exist in the
extragalactic space and analyze the consequences of their microlensing on light
from distant Active Galactic Nuclei. We find that such events have very similar
features to some observed Gamma Ray Bursts and use recent satellite data to set
an upper bound to the amount of negative mass in the universe.Comment: Essay awarded ``Honorable Mention'' in the Gravity Foundation
Research Awards, 199
Casimir invariants for the complete family of quasi-simple orthogonal algebras
A complete choice of generators of the center of the enveloping algebras of
real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is
obtained in a unified setting. The results simultaneously include the well
known polynomial invariants of the pseudo-orthogonal algebras , as
well as the Casimirs for many non-simple algebras such as the inhomogeneous
, the Newton-Hooke and Galilei type, etc., which are obtained by
contraction(s) starting from the simple algebras . The dimension of
the center of the enveloping algebra of a quasi-simple orthogonal algebra turns
out to be the same as for the simple algebras from which they come by
contraction. The structure of the higher order invariants is given in a
convenient "pyramidal" manner, in terms of certain sets of "Pauli-Lubanski"
elements in the enveloping algebras. As an example showing this approach at
work, the scheme is applied to recovering the Casimirs for the (3+1)
kinematical algebras. Some prospects on the relevance of these results for the
study of expansions are also given.Comment: 19 pages, LaTe
The 0.1-200 keV spectrum of the blazar PKS 2005-489 during an active state
The bright BL Lac object PKS 2005-489 was observed by BeppoSAX on November
1-2, 1998, following an active X-ray state detected by RossiXTE. The source,
detected between 0.1 and 200 keV, was in a very high state with a continuum
well fitted by a steepening spectrum due to synchrotron emission only. Our
X-ray spectrum is the flattest ever observed for this source. The different
X-ray spectral slopes and fluxes, as measured by various satellites, are
consistent with relatively little changes of the peak frequency of the
synchrotron emission, always located below 10^{17} Hz. We discuss these results
in the framework of synchrotron self-Compton models. We found that for the
BeppoSAX observation, the synchrotron peak frequency is between 10^{15} and
2.5x10^{16} Hz, depending on the model assumptions.Comment: 7 pages, 4 figures, accepted for publication in A&
Central extensions of the families of quasi-unitary Lie algebras
The most general possible central extensions of two whole families of Lie
algebras, which can be obtained by contracting the special pseudo-unitary
algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras
u(p,q), are completely determined and classified for arbitrary p,q. In addition
to the su(p,q) and u({p,q}) algebras, whose second cohomology group is well
known to be trivial, each family includes many non-semisimple algebras; their
central extensions, which are explicitly given, can be classified into three
types as far as their properties under contraction are involved. A closed
expression for the dimension of the second cohomology group of any member of
these families of algebras is given.Comment: 23 pages. Latex2e fil
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