Hopf Algebras Consisting of Finite Sets
Mai Zhou
TL;DR
This paper generalizes the Connes-Kreimer Hopf algebra from Feynman diagrams to finite sets, matrices, and star products, emphasizing the foundational role of finite sets in the construction.
Contribution
It introduces a new Hopf algebra structure based on finite sets, extending previous algebraic frameworks to more abstract mathematical objects.
Findings
Established a Hopf algebra structure on finite sets
Extended the algebraic framework to matrices and star products
Highlighted the importance of finite sets in algebraic constructions
Abstract
In this article we generalise the structure of Connes-Kreimer Hpof algebra consisting of Feynmam diagrams to the situations of abstract finite sets, matrices and star product of scalar field, where the construction for the case of finite sets is essential.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology