## Discrete Geometry and Combinatorics Seminar

Tamar FriedmannSmith College
The action of the symmetric group on a generalization of the free Lie algebra: a CataLAnKe Theorem
Monday, November 6, 2017 - 2:30pm
Malott 206

The free Lie algebra is a natural mathematical construction that is central in algebraic combinatorics and has applications in other fields. I will discuss a generalization of the free Lie algebra based on an $n$-ary commutator. The action of the symmetric group on its multilinear component generalizes the well-known representation $\mathrm{Lie}(k)$. I will discuss results and conjectures about this generalization of $\mathrm{Lie}(k)$, including a representation whose dimension is the Catalan number.