# Graded lie algebras of maximal class

Caranti, A., Mattarei, S. and Newman, M. F. (1997) Graded lie algebras of maximal class. Transactions of the American Mathematical Society, 349 (10). pp. 4021-4052. ISSN 0002-9947

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## Abstract

We study graded Lie algebras of maximal class over a field $\mathbf {F}$ of positive characteristic $p$. A. Shalev has constructed infinitely many pairwise non-isomorphic insoluble algebras of this kind, thus showing that these algebras are more complicated than might be suggested by considering only associated Lie algebras of p-groups of maximal class. Here we construct $| \mathbf {F}|^{\aleph _{0}}$ pairwise non-isomorphic such algebras, and $\max \{| \mathbf {F}|, \aleph _{0} \}$ soluble ones. Both numbers are shown to be best possible. We also exhibit classes of examples with a non-periodic structure. As in the case of groups, two-step centralizers play an important role

Keywords: Lie algebras, graded Lie algebra of maximal class G Mathematical and Computer Sciences > G100 Mathematics College of Science > School of Mathematics and Physics http://dx.doi.org/10.1090/S0002-9947-97-... 18520 07 Apr 2017 13:47

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