Texas A&M University, Department of Mathematics, 216 Milner Hall, 9th of March 2005, 3:00-3:50

Groups and Dynamics Seminar


Factorization of Hopf algebra characters

Marcelo Aguiar of Texas A&M University

The main result to be discussed is a non-commutative version of the following linear algebra result: if T is a linear transformation of order n (T^n=Id) on a vector space V, then T diagonalizes and the eigenvalues are the n-th roots of unity. In the non-commutative version, the role of V is played by the group of characters on a graded connected Hopf algebra, and the role of T by a canonical automorphism associated to the grading.

We will concentrate on the factorization corresponding to the Hopf algebra of quasi-symmetric functions and explain in what sense it is the universal case. The talk will be self-contained