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Some Factorizations in Universal Enveloping Algebras of Three Dimensional Lie Algebras and Generalizations |
Canad. Math. Bull. 45(2002), 525-536
Published:2002-12-01
Printed: Dec 2002
Printed: Dec 2002
- Stephen Berman
- Jun Morita
- Yoji Yoshii
Abstract
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.
| MSC Classifications: |
17B05 - Structure theory 17B35 - Universal enveloping (super)algebras [See also 16S30] 17B67 - Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B70 - Graded Lie (super)algebras |