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