The classification of [p]-nilpotent restricted Lie algebras of dimension 5

Darijani, Iren (2015) The classification of [p]-nilpotent restricted Lie algebras of dimension 5. Masters thesis, Memorial University of Newfoundland.

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Abstract

In this thesis, we will classify p-nilpotent restricted Lie algebras of dimension 5. Any finite dimensional p-nilpotent restricted Lie algebras is nilpotent by Engel’s theorem. Therefore, we use as our starting point, the classification of nilpotent Lie algebras of dimension 5 and classify the possible equivalence classes of p-maps on these Lie algebras. We first explain the method that we used to classify p-nilpotent restricted Lie algebras of dimension 5 which is the analogue of Skjelbred-Sund method for classifying nilpotent Lie algebras. Then, we will give a complete classification of p-nilpotent restricted Lie algebras of dimension 5 over perfect fields of characteristic p > 5.

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