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Casimir Operators and Nilpotent Radicals

Published online by Cambridge University Press:  20 November 2018

J. C. Ndogmo
J. C. Ndogmo*
Affiliation:
School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africae-mail: jean-claude.ndogmo@wits.ac.za
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Abstract

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It is shown that a Lie algebra having a nilpotent radical has a fundamental set of invariants consisting of Casimir operators. A different proof is given in the well known special case of an abelian radical. A result relating the number of invariants to the dimension of the Cartan subalgebra is also established.

Keywords

16W2517B4516S30nilpotent radicalCasimir operatorsalgebraic Lie algebrasCartan subalgebrasnumber of invariants
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 3 , 01 September 2012 , pp. 579 - 585
Copyright
Copyright © Canadian Mathematical Society 2012

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