Zeta functions of solvable Lie algebras over finite fields -- with calculations in detail

Abstract

Let $L$ be a solvable Lie algebra of dimension less than or equal to 4 over finite fields. We compute and record, in explicit symbolic form, the zeta functions enumerating subalgebras or ideals of $L$, and study their properties. We also discuss the implications of our data, in particular in relation to the general theory of Lie algebras over finite fields and zeta functions of Lie algebras over commutative rings.