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Classification of symbols of three-dimensional vector distributions of infinite type. (Russian. English summary) Zbl 06963938
Summary: 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 $$\geq3$$ 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 $$\dim\mathfrak{n}\leq5$$. This covers all such Lie algebras $$\mathfrak{m}$$ that $$\dim\mathfrak{m}\leq 7$$.
##### MSC:
 17B Lie algebras and Lie superalgebras
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##### References:
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