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Graded Lie Algebras of Maximal Class

A. Caranti, S. Mattarei and M. F. Newman
Transactions of the American Mathematical Society
Vol. 349, No. 10 (Oct., 1997), pp. 4021-4051
Stable URL: http://www.jstor.org/stable/2155574
Page Count: 31
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Graded Lie Algebras of Maximal Class
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Abstract

We study graded Lie algebras of maximal class over a field 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 |F|ℵ 0} pairwise non-isomorphic such algebras, and max{|F|,ℵ0} 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.

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