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Cartan Subalgebras of Zassenhaus Algebras

Published online by Cambridge University Press:  20 November 2018

Gordon Brown
Gordon Brown*
Affiliation:
University of Colorado, Boulder, Colorado
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Cartan subalgebras play a very important role in the classification of the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic zero. It is well-known [5, 273] that any two Cartan subalgebras of such an algebra are conjugate, i.e. images of one another under some automorphism of the algebra. On the other hand, there exist finitedimensional simple Lie algebras over fields of finite characteristic p possessing non-conjugate Cartan subalgebras [2; 3; 4]. The simple Lie algebras discovered by Zassenhaus [6] also possess non-conjugate Cartan subalgebras, and we shall give a complete classification of Cartan subalgebras of these algebras in this paper.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 1011 - 1021
Copyright
Copyright © Canadian Mathematical Society 1975

References

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