The fundamental notion of separability for commutative algebras was interpreted in categorical setting where also the stronger notion of heavily separability was introduced. These notions were extended to (co)algebras in monoidal categories, in particular to cowreaths. In this paper, we consider the cowreath (A⊗H4op,H4,ψ), where H4 is the Sweedler 4-dimensional Hopf algebra over a field k and A= Cl(α, β, γ) is the Clifford algebra generated by two elements G, X with relations G2= α, X2= β and XG+ GX= γ, (α, β, γ∈ k) which becomes naturally an H4-comodule algebra. We show that, when char (k) ≠ 2 , this cowreath is always separable and h-separable as well.
Separable Cowreaths Over Clifford Algebras
Menini C.
;
2023
Abstract
The fundamental notion of separability for commutative algebras was interpreted in categorical setting where also the stronger notion of heavily separability was introduced. These notions were extended to (co)algebras in monoidal categories, in particular to cowreaths. In this paper, we consider the cowreath (A⊗H4op,H4,ψ), where H4 is the Sweedler 4-dimensional Hopf algebra over a field k and A= Cl(α, β, γ) is the Clifford algebra generated by two elements G, X with relations G2= α, X2= β and XG+ GX= γ, (α, β, γ∈ k) which becomes naturally an H4-comodule algebra. We show that, when char (k) ≠ 2 , this cowreath is always separable and h-separable as well.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
