@book{9a4d12942dc54d9fbbe9e8f2e46e3a4d,

title = "On the structure of graded transitive Lie algebras",

abstract = "We study finite-dimensional Lie algebras ${\mathfrak L}$ of polynomial vector fields in $n$ variables that contain the vector fields $\dfrac{\partial}{\partial x_i} \; (i=1,\ldots, n)$ and $x_1\dfrac{\partial}{\partial x_1}+ \dots + x_n\dfrac{\partial}{\partial x_n}$. We show that the maximal ones always contain a semi-simple subalgebra $\bar{{\mathfrak g}}$, such that $\dfrac{\partial}{\partial x_i}\in \bar{{\mathfrak g}} \; (i=1,\ldots, m)$ for an $m$ with $1 \leq m \leq n$. Moreover a maximal algebra has no trivial $\bar{{\mathfrak g}}$-module in the space spanned by $\dfrac{\partial}{\partial x_i} (i=m+1,\ldots, n)$. The possible algebras $\bar{{\mathfrak g}}$ are described in detail, as well as all $\bar{{\mathfrak g}}$-modules that constitute such maximal ${\mathfrak L}$. All maximal ${\mathfrak L}$ are described explicitly for $n\leq 3$.",

keywords = "MSC-17B05, MSC-17B66, IR-65744, EWI-3377, MSC-17B70",

author = "Post, {Gerhard F.}",

note = "Imported from MEMORANDA",

year = "2000",

language = "Undefined",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1557",

}