Separable cowreaths in higher dimension

2025/06/23 by Renda, Fabio · 1 citation
#18M05 #Category Theory (math.CT) #FOS: Mathematics #Primary 16T05 #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Secondary 15A66

paper · doi:10.48550/arxiv.2506.18762

Abstract

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=H₄, Sweedler's Hopf algebra, the cowreath (A ⊗ H^op,H, ψ) is always (h-)separable. We show how to produce similar examples in higher dimension by considering a 2ⁿ⁺¹-dimensional Clifford algebra A=Cl(α,β_i,γ_i,λ_ij) and H=E(n), a suitable pointed Hopf algebra that generalizes H₄. 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.

Citations

• E(n)-coactions on semisimple Clifford algebras
• Heavily Separable Functors
• Frobenius and separable functors for the category of entwined modules over cowreaths, I: General theory
• Cocycle twisting of E(n)-module algebras and applications to the Brauer group
• On modules associated to coalgebra Galois extensions

Cited by

• On Separable and Frobenius Cowreaths of type (A ⊗ H^op, H,ψ)

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• New examples of separable cowreaths over Clifford algebras
• A Hopf algebra having a separable Galois extension is finite dimensional
• Heavily Separable Functors
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• Twisted separability for adjoint functors