The classification of 5-dimensional p-nilpotent restricted Lie algebras over perfect fields, I

We first adapt a method due to Skjelbred–Sund to classify p-nilpotent restricted Lie algebras. It turns out that any p-nilpotent restricted Lie algebra of dimension n can be constructed as a central extension of a p  -nilpotent restricted Lie algebra of dimension n−1n−1. We apply these techniques to classify all p  -nilpotent restricted Lie algebras of dimension 5 over a perfect field of characteristic p⩾5p⩾5.