Bi-College Math Colloquium

Monday, October 8, 2018 - 4:00pm

Tamar Friedmann

Haverford College

Given a vector space of matrices, one can impose a binary operation called a commutator, given by [A, B] = AB - BA. This operation satisfies a condition called the Jacobi identity, turning this vector space into what is known as a Lie algebra. In this talk, I will introduce the concept of a Lie algebra as well as generalizations thereof called Lie Algebras of the Third Kind (LATKes) or n-th kind (LAnKes). These algebras have associated vector spaces that admit an action of permutation groups. I will explain how, for certain classes of these vector spaces, the permutations lead to a new interpretation of the famous Catalan numbers which are central in algebraic combinatorics. I will then discuss some related open problems.