# 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 ${\partial}/{\partial x_i} \; (i=1,\ldots, n)$ 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 Enschede Department of Applied Mathematics, University of Twente Published - 1999

### Publication series

Name Department of Applied Mathematics, University of Twente 1503 0169-2690

### Fingerprint

Partial
Lie algebra
Polynomial vector fields
Finite dimensional algebra
Higher dimensions
Vector field

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

### Cite this

Post, G. F. (1999). On the structure of transitively differential algebras. Enschede: Department of Applied Mathematics, University of Twente.
Enschede : Department of Applied Mathematics, University of Twente, 1999.

Research output: Other research outputReport

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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 ${\partial}/{\partial x_i} \; (i=1,\ldots, n)$ 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.",
keywords = "MSC-17B66, EWI-3323, IR-65691, MSC-17B70, MSC-17B05",
author = "Post, {Gerhard F.}",
note = "Imported from MEMORANDA",
year = "1999",
publisher = "Department of Applied Mathematics, University of Twente",
number = "1503",

}

Post, GF 1999, On the structure of transitively differential algebras. Department of Applied Mathematics, University of Twente, Enschede.
Enschede : Department of Applied Mathematics, University of Twente, 1999.

Research output: Other research outputReport

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T1 - On the structure of transitively differential algebras

AU - Post,Gerhard F.

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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

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PB - Department of Applied Mathematics, University of Twente

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Post GF. On the structure of transitively differential algebras. Enschede: Department of Applied Mathematics, University of Twente, 1999.