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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rooted trees, Hopf algebras and rough paths
有根树 Hopf代数 粗路径
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2023/11/15
In this talk, we first recall some classical Hopf algebras on rooted trees, including Connes-Kreimer Hopf algebra and Loday-Ronco Hopf algebra. Then we give a combinatorial description of the coproduc...
A Pre-Lie algebra is a vector space L endowed with a bilinear product * : L \times L to L satisfying the relation (x*y)*z-x*(y*z)= (x*z)*y-x*(z*y), for all x,y,z in L. We give an explicit combinatoria...
We give a decomposition of triply rooted trees into three doubly rooted trees. This leads to a combinatorial interpretation of an identity conjectured by Lacasse in the study of the PAC-Bayesian machi...
On the conjugacy problem for finite-state automorphisms of regular rooted trees
finite-state automorphisms regular rooted trees math
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2010/11/15
We study the conjugacy problem in the automorphism group $Aut(T)$ of a regular rooted tree $T$ and in its subgroup $FAut(T)$ of finite-state automorphisms. We show that under the contracting conditio...
Towards cohomology of renormalization: bigrading the combinatorial Hopf algebra of rooted trees
bigrading the combinatorial Hopf algebra rooted trees
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2010/11/2
The renormalization of quantum field theory twists the antipode of a noncocommutative Hopf algebra of rooted trees, decorated by an infinite set of primitive divergences. The Hopf algebra of undecorat...