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 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 language | English |
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Pages (from-to) | 55-89 |
Number of pages | 35 |
Journal | Canadian Journal of Mathematics |
Volume | 67 |
Issue number | 1 |
DOIs | |
State | Published - 1 Feb 2015 |
Keywords
- Classification
- Filiform Lie algebras
- Graded Lie algebras
- Projective varieties
- Topology
ASJC Scopus subject areas
- General Mathematics