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Identities in the universal envelopes of Lie algelras

Published online by Cambridge University Press:  09 April 2009

Yu. A. Bachturin
Yu. A. Bachturin
Affiliation:
Department of Mathematics and Mechanics, Moscow State University, Moscow, USSR.
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It is well known (see Latyšev [1] for finite dimensional case) that the universal envelope of Lie Alaebra g over a commutative field ť of characteristic 0 is a PI-alaebra (i.e. possesses a nontrivial identity) if and only if this Lie algebra is abelian. On the other hand the recent results due to Passman [2] describe the conditions under which the group algebra of a group over an arbitrary commutative field is a PI-algebra. A. L. Šmel'kin suggested that I should find necessary and sufficient conditions for a Lie algebra g over a field of nonzero characteristic under which its universal envelope Ug should be a PI-algebra. These conditions are given in the following theorem.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 1 , August 1974 , pp. 10 - 21
Copyright
Copyright © Australian Mathematical Society 1974

References

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