Abstracts
for the Seminar

Fall 2017

**Speaker: **Tamar Friedmann, Smith College

**Title: **The action of the symmetric group on a generalization of the free Lie algebra: a CataLAnKe Theorem

**Time:** 2:30 PM, Monday, November 6, 2017

**Place:** Malott 206

**Abstract:** 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 Lie(k). I will discuss results and conjectures about this generalization of Lie(k), including a representation whose dimension is the Catalan number.

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