When are Hopf algebras determined by integer sequences?
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 $H$ and $K$ in this category under which there exists a surjective homomorphism from $H$ to $K$. We also give conditions such that an isomorphic copy of $H$ occurs as a Hopf subalgebra of $K$.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Advanced Topics in Algebra
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Journal of Pure and Applied Algebra
- Volume
- 230
- Issue
- 9
- Pages
- 108326–108326
- Publication date
- 13 June 2026
- Language
- EN