Hopf Algebras of B-Diagrams and Boson Normal Ordering: Exploring the Dual Structures
Combinatorics
2026-01-15 v1 Mathematical Physics
math.MP
Abstract
We consider the Hopf algebra of B-diagrams as an algebra projecting onto the Heisenberg algebra and designed to encode the combinatorics of the bosonic normal-ordering problem. In order to understand and generalize the properties of the algebra of noncommutative symmetric polynomials viewed as a Hopf subalgebra of the Hopf algebra linearly spanned by B-diagrams, we describe and study its dual Hopf algebra. This construction also allows us to establish connections with combinatorial Hopf algebras based on colored set partitions.
Keywords
Cite
@article{arxiv.2601.09357,
title = {Hopf Algebras of B-Diagrams and Boson Normal Ordering: Exploring the Dual Structures},
author = {Ali Chouria and Jean-Gabriel Luque},
journal= {arXiv preprint arXiv:2601.09357},
year = {2026}
}