Hostname: page-component-7bb8b95d7b-dtkg6 Total loading time: 0 Render date: 2024-09-18T10:14:47.463Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Albert, A. A.Structure of algebras (Amer. Math. Soc. Colloquium Publications, 1939).CrossRefGoogle Scholar
(2)Albert, A. A.Jordan algebras of linear transformations. Trans. Amer. math. Soc. 59 (1946), 524–55.CrossRefGoogle Scholar
(3)Jacobson, N.Rational methods in the theory of Lie algebras. Ann. Math., Princeton, (2), 36 (1935), 875–81.CrossRefGoogle Scholar
(4)Magnus, W.Über Bezeihungen zwischen höheren Kommutatoren. J. reine angew. Math. 177 (1937), 105–15.CrossRefGoogle Scholar