On the structure of transitively differential algebras

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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 languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente
Publication statusPublished - 1999

Publication series

PublisherDepartment of Applied Mathematics, University of Twente
ISSN (Print)0169-2690


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

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