When are Hopf algebras determined by integer sequences?
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918518356705280 |
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| author | Andrews, Nicolas Gagnon, Lucas Gélinas, Félix Schlums, Eric Zabrocki, Mike |
| author_facet | Andrews, Nicolas Gagnon, Lucas Gélinas, Félix Schlums, Eric Zabrocki, Mike |
| 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 $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When are Hopf algebras determined by integer sequences? Andrews, Nicolas Gagnon, Lucas Gélinas, Félix Schlums, Eric Zabrocki, Mike Combinatorics 16T30 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 $K$. |
| title | When are Hopf algebras determined by integer sequences? |
| topic | Combinatorics 16T30 |
| url | https://arxiv.org/abs/2505.06941 |