On bialgebras and Hopf algebras of oriented graphs
Dominique Manchon
TL;DR
This paper introduces two new coproducts for cycle-free oriented graphs, forming two commutative graded Hopf algebras with a comodule-coalgebra relationship, extending previous work on rooted trees.
Contribution
It generalizes the Hopf algebra structure from rooted trees to cycle-free oriented graphs by defining two coproducts and establishing their algebraic relations.
Findings
Constructed two commutative connected graded Hopf algebras
Established a comodule-coalgebra relationship between the two algebras
Extended previous results from rooted trees to cycle-free oriented graphs
Abstract
We define two coproducts for cycle-free oriented graphs, thus building up two commutative con- nected graded Hopf algebras, such that one is a comodule-coalgebra on the other, thus generalizing the result obtained previously for Hopf algebras of rooted trees.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology