The centre of a monoidal category is a braided monoidal category. Monoidal categories are monoidal objects (or pseudomonoids) in the monoidal bicategory of categories. This paper provides a universal construction in a braided monoidal bicategory that produces a braided monoidal object from any monoidal object. Some properties and sufficient conditions for existence of the construction are exami...

We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzezinski and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. We study the bosonisation of any braided group provides as a trivial principal bundle in three ways.

We construct double biproduct, bicrossproduct, double crossproduct, double bicrossproduct Lie bialgebras from braided Lie bialgebras. The relations between them are found. The main result generalizes Majid’s matched pair of Lie algebras, Drinfeld’s quantum double of Lie bialgebras, and Masuoka’s cross product Lie bialgebras. Some properties of double biproduct Lie bialgebras are given. In the a...

To some Hecke symmetries (i.e. Yang-Baxter braidings of Hecke type) we associate ”noncommutative varieties” called braided spheres. An example of such a variety is the Podles’ nonstandard quantum sphere. On any braided sphere we introduce and compute an ”equivariant” analogue of Connes’ noncommutative index. In contrast with the Connes’ construction our version of equivariant NC index is based ...

Abstract. Pleistocene braided-river deposits commonly represent long periods of non-deposition or erosion that are interrupted by rapid and short aggradation phases. When dating these sedimentary sequences with in situ-produced cosmic radionuclides (CRNs), simple concentration depth profiling approaches often fall short, as they assume the alluvial sequence has been deposited a constant rate ex...

We introduce a notion of " freely braided element " for simply laced Cox-eter groups. We show that an arbitrary group element w has at most 2 N (w) com-mutation classes of reduced expressions, where N(w) is a certain statistic defined in terms of the positive roots made negative by w. This bound is achieved if w is freely braided. In the type A setting, we show that the bound is achieved only f...