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Some Factorizations in Universal Enveloping Algebras of Three Dimensional Lie Algebras and Generalizations

Open Access article
 Printed: Dec 2002
  • Stephen Berman
  • Jun Morita
  • Yoji Yoshii
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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, 17B35, 17B67, 17B70 show english descriptions Structure theory
Universal enveloping (super)algebras [See also 16S30]
Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
Graded Lie (super)algebras
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

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