Test Sets and Test Rank of a Free Metabelian Lie Algebra

Abstract

We prove that the test rank of a free metabelian Lie algebra L of rank n equals n-1 and a test set of L belongs to the derived subalgebra of L.

Key Words:

• Free metabelian Lie algebra
• Test set
• Test rank

Acknowledgment

We thank the referee for pointing out that the same results have been independently proved by I. Chirkov and M. Shevelin in a paper entitled by “Test sets for free metabelian Lie algebras” accepted for publication by Siberian Math. J.