Caranti, A. and 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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Item Type: | Article |
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Item Status: | Live Archive |

## 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 |
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Subjects: | G Mathematical and Computer Sciences > G100 Mathematics |

Divisions: | College of Science > School of Mathematics and Physics |

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ID Code: | 18520 |

Deposited On: | 07 Apr 2017 13:47 |

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