Coquasitriangular Structure

A dual to the quasitriangular structure which is defined by the universal R-matrix [1]. Let be a Hopf algebra , where H is a vector space over , m and Δ are product and coproduct , ɛ and S are counit and antipode. A coquasitriangular structure is an invertible bilinear map such that

where the Heyneman–Sweedler notations [2] Δ a = ∑ a ₍₁₎ ⊗ a ₍₂₎ are used. The last equation is identical if the Hopf algebra is commutative and cocommutative . A twisted product , denoted by ○, is

(1)

being a special case of the Sweedler crossed product [3] that is associative, when is coquasitriangular.

The connection of the coquasitriangular structure with quantum fields [4] can be made identifying with the pairing, then the twisted product (1) coincides with the time-ordered product [5], which consistently leads to the Wick theorem [6]. In this context, renormalization is the replacement of a co quasitriangular structure by a more general 2- coboundary, and the set of “renormalized” 2-...