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

Published online by Cambridge University Press:  20 November 2018

Stephen Berman ,
Jun Morita  and
Yoji Yoshii
Stephen Berman
Affiliation:
Department of Mathematics University of Saskatchewan Saskatoon, Saskatchewan S7N 5E6, e-mail: berman@snoopy.usask.ca
Jun Morita
Affiliation:
Institute of Mathematics University of Tsukuba Tsukuba, Ibaraki 305-8571 Japan, e-mail: morita@math.tsukuba.ac.jp
Yoji Yoshii
Affiliation:
Department of Mathematics University of Alberta Edmonton, Alberta T6G 2G1, e-mail: yoshii@math.ualberta.ca
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Abstract

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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.

Keywords

17B0517B3517B6717B70
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 4 , 01 December 2002 , pp. 525 - 536
Copyright
Copyright © Canadian Mathematical Society 2002

References

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