It was recently shown by the authors that deformations of hypergroup convolutions w.r.t. positive semicharacters can be used to explain probabilistic connections between the Gelfand pairs (SL(d, C), SU(d)) and Hermitian matrices. We here study connections between general convolution semigroups on commutative hypergroups and their deformations. We are able to develop a satisfying theory, if the ...

We prove that any non L-cocommutative finite Markov L-coalgebra yields at least two solutions of the Yang-Baxter equation and therefore at least two representations of the braid groups. We conclude by a generalisation of these constructions to any coalgebra.

By means of graphical calculus we prove that, over fields of characteristic zero, any bialgebra deformation of the universal enveloping algebra of the algebra of traceless octonions satisfying the dual of the left and right Moufang identities must be coassociative and cocommutative.

Let H be a Hopf algebra with a bijective antipode over a commutative ring k with unit. The Brauer group of H is defined as the Brauer group of Yetter–Drinfel’d H-module algebras, which generalizes the Brauer–Long group of a commutative and cocommutative Hopf algebra and those known Brauer groups of structured algebras.

1.1. Background. This paper deals with the landmark results of Benson and Carlson's Projective resolutions and Poincar e duality complexes [6]. Our goal is to provide some necessary background for that work, and to prove some of the results of [6] in a more general setting. In particular, we analyze what happens when we replace Benson and Carlson's complex C (in the notation of [6]) with an arb...