Mathematics and Statistics Colloquium

Calvin University

Arnold Guikema and Madeline Lundberg
Calvin University

February 12, 2026
3:05pm   •   North Hall 276

Free Lie Algebras: Monomials and the Hall Basis

Free Lie algebras are a mathematical concept that have been explored for almost a century. Despite decades of research, the properties and behavior of one specific and useful basis for a free Lie algebra, the Hall basis, are still quite unknown. During the summer of 2025, we set out to explore properties of the Hall Basis and how these relate to free Lie algebras as a whole. Our results show how complexity can quickly arise from simple rules.