Separable cowreaths in higher dimension
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909657517260800 |
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| author | Renda, Fabio |
| author_facet | Renda, Fabio |
| contents | In this paper we present an infinite family of (h-)separable cowreaths with increasing dimension. Menini and Torrecillas proved in [20] that for $A=Cl(α,β, γ)$, a four-dimensional Clifford algebra, and $H=H_4$, Sweedler's Hopf algebra, the cowreath $(A \otimes H^{op},H, ψ)$ is always (h-)separable. We show how to produce similar examples in higher dimension by considering a $2^{n+1}$-dimensional Clifford algebra $A=Cl(α,β_i,γ_i,λ_{ij})$ and $H=E(n)$, a suitable pointed Hopf algebra that generalizes $H_4$. We adopt the approach pursued in [19], requiring that the separability morphism be of a simplified form, which in turn forces the defining scalars $α,β_i,γ_i,λ_{ij}$ to satisfy further conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_18762 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Separable cowreaths in higher dimension Renda, Fabio Quantum Algebra Category Theory Rings and Algebras Primary 16T05, Secondary 15A66, 18M05 In this paper we present an infinite family of (h-)separable cowreaths with increasing dimension. Menini and Torrecillas proved in [20] that for $A=Cl(α,β, γ)$, a four-dimensional Clifford algebra, and $H=H_4$, Sweedler's Hopf algebra, the cowreath $(A \otimes H^{op},H, ψ)$ is always (h-)separable. We show how to produce similar examples in higher dimension by considering a $2^{n+1}$-dimensional Clifford algebra $A=Cl(α,β_i,γ_i,λ_{ij})$ and $H=E(n)$, a suitable pointed Hopf algebra that generalizes $H_4$. We adopt the approach pursued in [19], requiring that the separability morphism be of a simplified form, which in turn forces the defining scalars $α,β_i,γ_i,λ_{ij}$ to satisfy further conditions. |
| title | Separable cowreaths in higher dimension |
| topic | Quantum Algebra Category Theory Rings and Algebras Primary 16T05, Secondary 15A66, 18M05 |
| url | https://arxiv.org/abs/2506.18762 |