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Automorphisms of Free Nilpotent Lie Algebras

Published online by Cambridge University Press:  20 November 2018

Vesselin Drensky  and
C. K. Gupta
Vesselin Drensky
Affiliation:
Bulgarian Academy of Sciences, Sofia, Bulgaria
C. K. Gupta
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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Let Fm be the free Lie algebra of rank m over a field K of characteristic 0 freely generated by the set ﹛x1,… ,xm﹜, m ≧ 2. Cohn [7] proved that the automorphism group Aut Fm of the K-algebra Fm is generated by the following automorphisms: (i) automorphisms which are induced by the action of the general linear group GLm (= GLm(K)) on the subspace of Fm spanned by ﹛x1, … ,xm﹜; (ii) automorphisms of the form x1 → x1 +f(x2,… ,xm),Xk → xk, k ≠ 1, where the polynomial f(x2,…,xm) does not depend on x1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 2 , 01 April 1990 , pp. 259 - 279
Copyright
Copyright © Canadian Mathematical Society 1990

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