Computing the automorphism group of a solvable Lie algebra

Abstract

We describe an effective algorithm for computing the automorphism group of a finite-dimensional solvable Lie algebra over a finite field. We show that a similar approach can be used to determine a canonical table for such a Lie algebra; that is, a description for the Lie algebra which is invariant under isomorphisms. Hence we also obtain an effective isomorphism test for finite-dimensional solvable Lie algebras over finite fields.