We consider a modified version of the coproduct for U(suq(2)) and show that in the limit when q → 1, there exists an essentially non-cocommutative coproduct. We study the implications of this non-cocommutativity for a system of two spin-1/2 particles. Here it is shown that, unlike the usual case, this non-trivial coproduct allows for symmetric and antisymmetric states to be present in the multi...

The q-Poincaré group of [1] is shown to have the structure of a semidirect product and coproduct B>⊳ ̃ SOq(1, 3) where B is a braided-quantum group structure on the q-Minkowski space of 4-momentum with braided-coproduct ∆p = p⊗ 1+1⊗p. Here the necessary B is not a usual kind of quantum group, but one with braid statistics. Similar braided-vectors and covectors V (R), V (R) exist for a general R...

Multiplication and comultiplication of beliefs represent a generalisation of multiplication and comultiplication of probabilities as well as of binary logic AND and OR. Our approach follows that of subjective logic, where belief functions are expressed as opinions that are interpreted as being equivalent to beta probability distributions. We compare different types of opinion product and coprod...

We define a Hopf algebra of motivic iterated integrals on the line and prove an explicit formula for the coproduct ∆ in this Hopf algebra. We show that this formula encodes the group law of the automorphism group of a certain noncommutative variety. We relate the coproduct ∆ with the coproduct in the Hopf algebra of decorated rooted plane trivalent trees, which is a plane decorated version of t...

It is by now well known that the Poincaré group acts on the Moyal plane with a twisted coproduct. Poincaré invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincaré action in quantum theories on the Moyal plane. We develop quantum field theories invariant under the twisted action from the representations of the...