On varieties of Lie algebras of maximal class

Tatyana Barron, Dmitry Kerner, Marina Tvalavadze

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5 Scopus citations


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 there are only three isomorphism types of N-graded Lie algebras L = ⊕i=l Li of maximal class generated by Li and L2L = (L1, L2). Vergne described the structure of these algebras with the property L = (L1). In this paper we study those generated by the first and q-th components where q > 2, L = (Ll, Lq). 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.

Original languageEnglish
Pages (from-to)55-89
Number of pages35
JournalCanadian Journal of Mathematics
Issue number1
StatePublished - 1 Feb 2015


  • Classification
  • Filiform Lie algebras
  • Graded Lie algebras
  • Projective varieties
  • Topology

ASJC Scopus subject areas

  • General Mathematics


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