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

Thoughts on Tachyon Cosmology

After a pedagogical review of elementary cosmology, I go on to discuss some obstacles to obtaining inflationary or accelerating universes in M/String Theory. In particular, I give an account of an old No-Go Theorem to this effect. I then describe some recent ideas about the possible r\^ole of the tachyon in cosmology. I stress that there are many objections to a naive inflationary model based on the tachyon, but there remains the possiblity that the tachyon was important in a possible pre-inflationary Open-String Era preceding our present Closed String Era.Comment: 34 pages, no figures. This is the written version of a lecture delivered at the Workshop on the Quantum Structure of Spacetime and the Geometric Nature of Fundamental Interactions held in Leuven from Sept 13th to Sept 19th(2002) which is to appear in the Proceedings in a special issue of Quantum and Classical Gravit

Nurses' perceptions of aids and obstacles to the provision of optimal end of life care in ICU

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