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Note on nilpotent and solvable algebras

Published online by Cambridge University Press:  24 October 2008

E. M. Patterson
E. M. Patterson
Affiliation:
Department of Mathematics United CollegeUniversity of St Andrews
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Extract

In general, the class of a nilpotent linear algebra of dimension n is at most n + 1, and the index, or derived length, of a solvable linear algebra of dimension n is at most n. In this note it is shown that, for a nilpotent linear algebra of dimension n satisfying x2 = 0 for all x, the class is at most n; and bounds are obtained for the indices of solvable Lie algebras.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 1 , January 1955 , pp. 37 - 40
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

REFERENCES

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