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THE GROUP OF AUTOMORPHISMS OF THE LIE ALGEBRA OF DERIVATIONS OF A FIELD OF RATIONAL FUNCTIONS

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  10 June 2016

V. V. BAVULA
V. V. BAVULA*
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom e-mail: v.bavula@sheffield.ac.uk
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Abstract

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We prove that the group of automorphisms of the Lie algebra DerK(Qn) of derivations of the field of rational functions Qn = K(x1, . . ., xn) over a field of characteristic zero is canonically isomorphic to the group of automorphisms of the K-algebra Qn.

MSC classification

Primary: 17B40: Automorphisms, derivations, other operators
Secondary: 17B20: Simple, semisimple, reductive (super)algebras 17B66: Lie algebras of vector fields and related (super) algebras 17B65: Infinite-dimensional Lie (super)algebras 17B30: Solvable, nilpotent (super)algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 3 , September 2017 , pp. 513 - 524
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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