Hongdi Huang, Department of Pure Mathematics, & William Dugan, Department of Combinatorics & Optimization, University of Waterloo
"An introduction to Kreimer's Hopf algebra and Grossman-Larson Hopf algebra"
The Hopf algebra of rooted trees is introduced in Connes and Kreimer [1988], in the context of Quantum Field Theory. Considering the vector space with a basis consisting of rooted trees, then define different multiplications and coproducts to make it into different Hopf algebras. In this talk, we will introduce Kreimer's Hopf algebra and Grossman-Larson Hopf algebra. We will also conclude a description of the isomorphism between the graded dual of Kreimer's Hopf algebra and Grossman-Larson Hopf algebra. The main references will be the paper "Combinatorics of Rooted Trees and Hopf Algebras", by M. Hoffman and "An introduction to Hopf algebras of trees", by Foissy.
MC 5501