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Abstract

Speaker: Marcelo Aguiar, Texas A&M University

Title: Factorization of Hopf algebra characters

Abstract:

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. These notions will be defined and illustrated with several examples.

The factorization corresponding to the Hopf algebra of quasi-symmetric functions will be one of the main focuses. It involves interesting combinatorial constructions and allows for various applications.



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