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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

REFERENCES

1. Bavula, V. V., Every monomorphism of the Lie algebra of triangular polynomial derivations is an automorphism, C. R. Acad. Sci. Paris, Ser. I, 350 (11–12) (2012), 553–556. (Arxiv:math.AG:1205.0797)CrossRefGoogle Scholar
2. Bavula, V. V., Lie algebras of triangular polynomial derivations and an isomorphism criterion for their Lie factor algebras, Izvestiya: Math. 77 (6) (2013), 3–44. (Arxiv:math.RA:1204.4908)Google Scholar
3. Bavula, V. V., The groups of automorphisms of the Lie algebras of triangular polynomial derivations, J. Pure Appl. Algebra 218 (2014), 829–851. (Arxiv:math.AG/1204.4910)Google Scholar
4. Bavula, V. V., The group of automorphisms of the Lie algebra of derivations of a polynomial algebra, Arxiv:math.RA:1304.6524. J. Algebra and Its Appl. (2016), to appear.Google Scholar
5. Bavula, V. V., The groups of automorphisms of the Witt Wn and Virasoro Lie algebras, Arxiv:math.RA:1304.6578. Chech. J. Math. (2016), to appear.Google Scholar
6. Freudenburg, G., Algebraic theory of locally nilpotent derivations, Encyclopaedia of Mathematical Sciences, vol. 136. Invariant Theory and Algebraic Transformation Groups, VII (Springer-Verlag, Berlin, 2006), 261.Google Scholar
7. Nowicki, A., Polynomial derivations and their rings of constants (Uniwersytet, Mikolaja Kopernika, Torun, 1994).Google Scholar
8. Osborn, J. M., Automorphisms of the Li algebras W* in characteristic zero, Can. J. Math. 49 (1997), 119–132.Google Scholar
9. Rudakov, A. N., Automorphism groups of infinite-dimensional simple Lie algebras, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 748–764.Google Scholar
10. Rudakov, A. N., Subalgebras and automorphisms of Lie algebras of Cartan type, Funktsional. Anal. i Prilozhen. 20 (1) (1986), 83–84.Google Scholar
11. van den Essen, A., Polynomial automorphisms and the Jacobian conjecture, Progress in Mathematics, vol. 190 (Birkhäuser Verlag, Basel, 2000), 329.Google Scholar
12. Zhao, K., Isomorphisms between generalized Cartan type W Lie algebras in characteristic zero, Can. J. Math. 50 (1998), 210–224.Google Scholar