Journal of Lie Theory Vol. 12, No. 1, pp. 265288 (2002) 

On the Structure of Graded Transitive Lie AlgebrasGerhard PostGerhard PostFaculty of Mathematical Sciences University Twente P.O. Box 217 7500 AE Enschede, The Netherlands post@math.utwente.nl Abstract: We study finitedimensional Lie algebras $\L$ of polynomial vector fields in $n$ variables that contain the vector fields ${{\partial}\over{\partial x_i}} \; (i=1,\ldots, n)$ and $x_1{{\partial}\over{\partial x_1}}+ \dots + x_n{{\partial}\over{\partial x_n}}$. We show that the maximal ones always contain a semisimple subalgebra $\gs$, such that ${{\partial}\over{\partial x_i}}\in \gs \; (i=1,\ldots, m)$ for an $m$ with $1 \leq m \leq n$. Moreover a maximal algebra has no trivial $\gs$modules in the space spanned by ${{\partial}\over{\partial x_i}} (i=m+1,\ldots, n)$. The possible algebras $\gs$ are described in detail, as well as all $\gs$modules that constitute such maximal $\L$. The maximal algebras are described explicitly for $n\leq 3$. Keywords: Lie algebras, vector fields, graded Lie algebras Classification (MSC2000): 17B66, 17B70, 17B05 Full text of the article:
Electronic fulltext finalized on: 30 Oct 2001. This page was last modified: 9 Nov 2001.
© 2001 Heldermann Verlag
