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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.06941 |
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Table of Contents:
- 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 $K$.