Isotopism and isomorphism classes of certain Lie algebras over finite fields

Abstract

In the current paper, we study the distribution into isotopism and isomorphism classes of the relevant family FpnFnp of Lie algebras of basis {e1,…,en}{e1,…,en} and nonzero brackets [ei,en]∈⟨e1,…,en−1⟩[ei,en]∈⟨e1,…,en−1⟩ over a finite field FpFp , with p prime. At this end we first introduce the concept of the structure tuple of a Lie algebra and specifically prove that there exist n isotopism classes in FpnFnp and three families of isomorphism classes depending on the first component of their structure tuple.