UM Math Graduate Students Seminar

Rafael S. González D'León
University of Miami

will present

The combinatorial structure behind multibracketed free Lie algebras

Friday, January 31, 2014, 2:30pm
Ungar Building Room 506

Abstract:We explore a beautiful interaction between algebra and combinatorics in the heart of the free Lie algebra on n generators: The multilinear component of the free Lie algebra Lie(n) is isomorphic as a representation of the symmetric group to the top cohomology of the poset of partitions of an n-set tensored with the sign representation. Then we can understand the algebraic object Lie(n) by applying poset theoretic techniques to the poset of partitions whose description is purely combinatorial. We will show how this relation generalizes further in order to study free Lie algebras with multiple compatible brackets. In particular we obtain combinatorial bases and compute the dimensions of these modules. Part of the talk is based on joint work with M. Wachs (UM).

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