Dual of the Hopf Algebra Consisting of the Adjacency Matrices
Zhou Mai
TL;DR
This paper explores two Hopf algebra structures based on adjacency matrices, revealing their relation to the Connes-Kreimer Hopf algebra and its dual, thus advancing algebraic understanding of graph-related structures.
Contribution
It identifies and analyzes two distinct Hopf algebra structures on adjacency matrices, linking them to the Connes-Kreimer algebra and its dual, which was not previously established.
Findings
Established a Hopf algebra structure identical to the Connes-Kreimer algebra.
Identified a dual Hopf algebra structure related to the Connes-Kreimer algebra.
Provided detailed algebraic properties of adjacency matrix-based Hopf algebras.
Abstract
In this article we discuss the Hopf algebras spanned by the adjacency matrices in detail. We show that there two Hopf algebraic structures concerning the adjacency matrices, one is the copy of Connes-Kreimer Hopf algebra, another one is the copy of the dual of Connes-Kreimer Hopf algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons