On the structure of transitively differential algebras

Gerhard F. Post

On the structure of transitively differential algebras

Gerhard F. Post

Discrete Mathematics and Mathematical Programming

Research output: Book/Report › Report › Other research output

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Abstract

We study finite-dimensional Lie algebras of polynomial vector fields in $n$ variables that contain the vector fields ${\partial}/{\partial x_i} \; (i=1,\ldots, n)$ and $x_1{\partial}/{\partial x_1}+ \dots + x_n{\partial}/{\partial x_n}$. We derive some general results on the structure of such Lie algebras, and provide the complete classification in the cases $n=2$ and $n=3$. Finally we describe a certain construction in high dimensions.

Original language	Undefined
Place of Publication	Enschede
Publisher	University of Twente
Publication status	Published - 1999

Publication series

Name
Publisher	Department of Applied Mathematics, University of Twente
No.	1503
ISSN (Print)	0169-2690

Keywords

MSC-17B66
EWI-3323
IR-65691
MSC-17B70
MSC-17B05

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Cite this

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title = "On the structure of transitively differential algebras",

abstract = "We study finite-dimensional Lie algebras of polynomial vector fields in \$n\$ variables that contain the vector fields \$\{\textbackslash{}partial\}/\{\textbackslash{}partial x\_i\} \textbackslash{}; (i=1,\textbackslash{}ldots, n)\$ and \$x\_1\{\textbackslash{}partial\}/\{\textbackslash{}partial x\_1\}+ \textbackslash{}dots + x\_n\{\textbackslash{}partial\}/\{\textbackslash{}partial x\_n\}\$. We derive some general results on the structure of such Lie algebras, and provide the complete classification in the cases \$n=2\$ and \$n=3\$. Finally we describe a certain construction in high dimensions.",

keywords = "MSC-17B66, EWI-3323, IR-65691, MSC-17B70, MSC-17B05",

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

note = "Imported from MEMORANDA",

year = "1999",

language = "Undefined",

publisher = "University of Twente",

number = "1503",

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TY - BOOK

T1 - On the structure of transitively differential algebras

AU - Post, Gerhard F.

N1 - Imported from MEMORANDA

PY - 1999

Y1 - 1999

N2 - We study finite-dimensional Lie algebras of polynomial vector fields in $n$ variables that contain the vector fields ${\partial}/{\partial x_i} \; (i=1,\ldots, n)$ and $x_1{\partial}/{\partial x_1}+ \dots + x_n{\partial}/{\partial x_n}$. We derive some general results on the structure of such Lie algebras, and provide the complete classification in the cases $n=2$ and $n=3$. Finally we describe a certain construction in high dimensions.

AB - We study finite-dimensional Lie algebras of polynomial vector fields in $n$ variables that contain the vector fields ${\partial}/{\partial x_i} \; (i=1,\ldots, n)$ and $x_1{\partial}/{\partial x_1}+ \dots + x_n{\partial}/{\partial x_n}$. We derive some general results on the structure of such Lie algebras, and provide the complete classification in the cases $n=2$ and $n=3$. Finally we describe a certain construction in high dimensions.

KW - MSC-17B66

KW - EWI-3323

KW - IR-65691

KW - MSC-17B70

KW - MSC-17B05

M3 - Report

BT - On the structure of transitively differential algebras

PB - University of Twente

CY - Enschede

ER -