When are Hopf algebras determined by integer sequences?
Combinatorics
2026-05-25 v2
Abstract
We study the category of graded Hopf algebras that are free noncommutative, cocommutative, graded and connected from the perspective of the sequences of dimensions of the graded pieces. We show that a Hopf algebra exists with a given sequence of graded dimensions if and only if the ``INVERTi'' transformation of the sequence is nonnegative. We give conditions on the sequences of graded dimensions for two Hopf algebras and in this category under which there exists a surjective homomorphism from to . We also give conditions such that an isomorphic copy of occurs as a Hopf subalgebra of .
Cite
@article{arxiv.2505.06941,
title = {When are Hopf algebras determined by integer sequences?},
author = {Nicolas Andrews and Lucas Gagnon and Félix Gélinas and Eric Schlums and Mike Zabrocki},
journal= {arXiv preprint arXiv:2505.06941},
year = {2026}
}