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 $K$.
| Subjects: | Combinatorics (math.CO) |
| MSC classes: | 16T30 |
| Cite as: | arXiv:2505.06941 [math.CO] |
| (or arXiv:2505.06941v2 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2505.06941 arXiv-issued DOI via DataCite |
From: Mike Zabrocki [view email]
[v1]
Sun, 11 May 2025 11:13:50 UTC (38 KB)
[v2]
Fri, 22 May 2026 17:34:27 UTC (37 KB)
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