Journal of Lie Theory 12 (2002), No. 2, 503--514
Copyright Heldermann Verlag 2002
On a Family of Operators and their Lie Algebras
Jan A. Sanders
Division of Mathematics and Computer Science, Faculty of Science, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
Jing Ping Wang
Division of Mathematics and Computer Science, Faculty of Science, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
An infinite family of differential operators is constructed. Each of these operators defines a Lie bracket and the operator is a homomorphism from the new Lie algebra to the standard Lie algebra. An interesting feature of these operators is that they factorize into first order operators with integer coefficients. This generalizes recent results of Zhiber and Sokolov.
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