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 Tr. Inst. Mat., 2012, Volume 20, Number 1, Pages 83–95 (Mi timb165)

Classification of symbols of three-dimensional vector distributions of infinite type

Institute of Mathematics of the National Academy of Sciences of Belarus

Abstract: We consider non-degenerate fundamental Lie algebras $\mathfrak{m}$ of infinite type over an arbitrary field of zero characteristic that can be uniquely represented as special extensions $0\to\mathfrak{a}\to\mathfrak{m}\to\mathfrak{n}\to0$, where all homogeneous components of $\mathfrak{a}$ are of dimension one. We provide explicit description of all such extensions in cases when $\mathfrak{n}$ is either a contact Lie algebra of dimension $\ge3$ or five-dimensional nilpotent Lie algebra of type $G_2$. In particular, get all fundamental Lie algebras $\mathfrak{m}$ of infinite type with $\dim\mathfrak{m}_{-1}=3$ and $\dim\mathfrak{n}\le5$. This covers all such Lie algebras $\mathfrak{m}$ that $\dim\mathfrak{m}\le 7$.

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UDC: 512.818.4, 514.763.8

Citation: O. Yu. Radko, “Classification of symbols of three-dimensional vector distributions of infinite type”, Tr. Inst. Mat., 20:1 (2012), 83–95

Citation in format AMSBIB
\Bibitem{Rad12} \by O.~Yu.~Radko \paper Classification of symbols of three-dimensional vector distributions of infinite type \jour Tr. Inst. Mat. \yr 2012 \vol 20 \issue 1 \pages 83--95 \mathnet{http://mi.mathnet.ru/timb165}