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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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