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Search: MSC category 17B67 ( Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras )

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1. CMB 2002 (vol 45 pp. 525)

Berman, Stephen; Morita, Jun; Yoshii, Yoji
Some Factorizations in Universal Enveloping Algebras of Three Dimensional Lie Algebras and Generalizations
We introduce the notion of Lie algebras with plus-minus pairs as well as regular plus-minus pairs. These notions deal with certain factorizations in universal enveloping algebras. We show that many important Lie algebras have such pairs and we classify, and give a full treatment of, the three dimensional Lie algebras with plus-minus pairs.

Categories:17B05, 17B35, 17B67, 17B70

2. CMB 2002 (vol 45 pp. 606)

Gannon, Terry
Postcards from the Edge, or Snapshots of the Theory of Generalised Moonshine
We begin by reviewing Monstrous Moonshine. The impact of Moonshine on algebra has been profound, but so far it has had little to teach number theory. We introduce (using `postcards') a much larger context in which Monstrous Moonshine naturally sits. This context suggests Moonshine should indeed have consequences for number theory. We provide some humble examples of this: new generalisations of Gauss sums and quadratic reciprocity.

Categories:11F22, 17B67, 81T40

3. CMB 2002 (vol 45 pp. 623)

Gao, Yun
Fermionic and Bosonic Representations of the Extended Affine Lie Algebra $\widetilde{\mathfrak{gl}_N} (\mathbb{C}_q)$
We construct a class of fermions (or bosons) by using a Clifford (or Weyl) algebra to get two families of irreducible representations for the extended affine Lie algebra $\widetilde{\mathfrak{gl}_N (\mathbb{C}_q)}$ of level $(1,0)$ (or $(-1,0)$).

Categories:17B65, 17B67

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