Expand all Collapse all | Results 1 - 3 of 3 |
1. CMB 2002 (vol 45 pp. 525)
Some Factorizations in Universal Enveloping Algebras of Three Dimensional Lie Algebras and Generalizations |
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)
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)
Fermionic and Bosonic Representations of the Extended Affine Lie Algebra $\widetilde{\mathfrak{gl}_N} (\mathbb{C}_q)$ |
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 |