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 $\Bbb Z_2$-, $\Bbb Z_3$-, and $\Bbb Z_2\otimes\Bbb Z_2$-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 $su(3)$, 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 $\hat A_2$ 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 $so(p,q)$, as well as the Casimirs for many non-simple algebras such as the inhomogeneous $iso(p,q)$, the Newton-Hooke and Galilei type, etc., which are obtained by contraction(s) starting from the simple algebras $so(p,q)$. 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 $so(p,q)$ 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