For a locally compact group G, the measure convolution algebra M(G) carries a natural coproduct. In previous work, we showed that the canonical predual C0(G) of M(G) is the unique predual which makes both the product and the coproduct on M(G) weak∗-continuous. Given a discrete semigroup S, the convolution algebra l(S) also carries a coproduct. In this paper we examine preduals for l(S) making b...

Yang’s theorem forbids the process Z → 2γ in any Poincaré invariant theory if photons are bosons and their two-particle states transform under the Poincaré group in the standard way (under the standard coproduct of the Poincaré group). This is an important result as it does not depend on the assumptions of quantum field theory. Recent work on noncommutative geometry requires deforming the above...

This paper argues that the core of modularity problems is an understanding of how individual components of a large system interact with each other, and that this interaction can be described by a layer structure. We propose a uniform treatment of layers based upon the concept of a monad. The combination of different systems can be described by the coproduct of monads. Concretely, we give a cons...

In a recent paper [1], a systematic construction of integrable Hamiltonians with coalgebra symmetry has been proposed. Such procedure can be applied to any Poisson coalgebra (A,∆) with generators Xi, i = 1, . . . , l and Casimir element C(X1, . . . , Xl) as follows. Let us consider the N -th coproduct ∆(Xi) of the generators and the m-th order (2 ≤ m ≤ N) coproducts ∆(m)(C) of the Casimir opera...

We first construct and give basic properties of the fibered coproduct in the category of ringed spaces. We then look at some special cases where this actually gives a fibered coproduct in the category of schemes. Intuitively this is gluing a collection of schemes along some collection of subschemes. We then use this to construct a scheme without closed points.

Let HH be an algebra with a distinguished element εH∈H∗εH∈H∗ and C,DC,D two coalgebras. Based on the construction of Brzeziński’s crossed coproduct, under some suitable conditions, we introduce coassociative coalgebra C×GTHβR×DC×TGHRβ×D which is more general two-sided coproduct structure including smash coproduct. Necessary sufficient conditions for equipped tensor product C⊗H⊗DC⊗H⊗D to bialgeb...

Exact supersymmetry can be maintained on non-anticommutative superspace with a twisted coproduct on the supergroup.We show that the usual exchange statistics for the superfields is not compatible with the twisted action of the superpoincaré group and find a statistics which is consistent with the twisted coproduct and imply interesting phenomena such as mixing of fermions and bosons under parti...

We construct an operad Phyl whose operations are the edge-labelled trees used in phylogenetics. This operad is the coproduct of Com, the operad for commutative semigroups, and [0,∞), the operad with unary operations corresponding to nonnegative real numbers, where composition is addition. We show that there is a homeomorphism between the space of n-ary operations of Phyl and Tn × [0,∞)n+1, wher...

We formulate the Hopf algebra underlying the su(2|2) S-matrix relevant for the AdS/CFT correspondence, extending the one discovered by Janik in the su(1|2) sector to the full algebra, by specifying the action of the coproduct and the antipode on the remaining generators. The nontriviality of the coproduct is determined by the lenght-changing effect, and results in an unusual central braiding. W...