For every field F which has a quadratic extension E we show there are non-metabelian infinite-dimensional thin graded Lie algebras all of whose homogeneous components, except the second one, have dimension 2. We construct such Lie algebras as F-subalgebras of Lie algebras M of maximal class over E. We characterise the thin Lie F-subalgebras of M generated in degree 1. Moreover we show that every thin Lie algebra L whose ring of graded endomorphisms of degree zero of L3 is a quadratic extension of F can be obtained in this way. We also characterise the 2- generator F-subalgebras of a Lie algebra of maximal class over E which are ideally r-constrained for a positive integer r.

THIN SUBALGEBRAS OF LIE ALGEBRAS OF MAXIMAL CLASS

M. AVITABILE;A. CARANTI;N. GAVIOLI;V. MONTI;
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Abstract

For every field F which has a quadratic extension E we show there are non-metabelian infinite-dimensional thin graded Lie algebras all of whose homogeneous components, except the second one, have dimension 2. We construct such Lie algebras as F-subalgebras of Lie algebras M of maximal class over E. We characterise the thin Lie F-subalgebras of M generated in degree 1. Moreover we show that every thin Lie algebra L whose ring of graded endomorphisms of degree zero of L3 is a quadratic extension of F can be obtained in this way. We also characterise the 2- generator F-subalgebras of a Lie algebra of maximal class over E which are ideally r-constrained for a positive integer r.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/169371
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