Factorizations in Universal Enveloping algebras of three dimensional Lie algebras and generalizations
S. Berman, J. Morita, Y. 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.
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