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arXiv · 1403.5793

On varieties of Lie algebras of maximal class

Tatyana Barron·Dmitry Kerner·Marina Tvalavadze
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Abstract

We study complex projective varieties that parametrize (finite-dimensional) filiform Lie algebras over C, using equations derived by Millionshchikov. In the infinite-dimensional case we concentrate our attention on N-graded Lie algebras of maximal class. As shown by A. Fialowski (see also [shalev:97], [millionshchikov:04]) there are only three isomorphism types of N-graded Lie algebras $L=\oplus^{\infty}_{i=1} L_i$ of maximal class generated by L_1 and L_2, L= . Vergne described the structure of these algebras with the property L= . In this paper we study those generated by the first and q-th components where q>2, L= . Under some technical condition, there can only be one isomorphism type of such algebras. For q=3 we fully classify them. This gives a partial answer to a question posed by Millionshchikov.

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Tatyana Barron, Dmitry Kerner, Marina Tvalavadze. 2014-03-23. On varieties of Lie algebras of maximal class. https://doi.org/10.4153/cjm-2014-008-x

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