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On the automorphism groups of certain Lie algebras

Published online by Cambridge University Press:  24 October 2008

Dan Segal
Dan Segal
Affiliation:
All Souls College, Oxford 0X1 4AL
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Extract

We fix a ground field k and a finite separable extension K of k. To a Lie algebra L over k is associated the Lie algebra KL = K ⊗kL over K. If we forget the action of K, we can think of KL as a larger Lie algebra over k; in particular we can ask what is the automorphism group Autk KL of KL as a k-algebra. There does not seem to be any simple answer to this question in general; the purpose of this note is to give a simple condition on L which makes Autk KL quite easy to determine. Examples of algebras which satisfy this condition include the free nilpotent Lie algebras and the algebras of all n × n triangular nilpotent matrices.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 1 , July 1989 , pp. 67 - 76
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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