We show how to construct central and grouplike quantum determinants for FRT algebras A(R). As an application of the general construction we give a quantum determinant for the q-Lorentz group.

Two antigens, the group-specific carbohydrate and the Type II carbohydrate, have been isolated by cellulose column chromatography from a formamide extract of a Group F streptococcus. Chemical and immunologic analyses indicate that both antigens are free of other cellular components. Both antigens are components of the cell wall although the Type II antigen is probably more superficial than the ...

A relationship between coseparable corings and separable non-unital rings is established. In particular it is shown that an A-coring C has an associative A-balanced product. A Morita context is constructed for a coseparable coring with a grouplike element. Biseparable corings are defined, and a conjecture relating them to Frobenius corings is proposed.

Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the Cuntz-Quillen theorem relating existence of connections in a module to projectivity of this module is proven.

This is the text of a talk given at the Isaac Newton Institute in Cambridge on 4th August, 2006. This talk is motivated by a recent paper [A Kaygun and M Khalkhali, Hopf modules and noncommutative differential geometry, Lett. Math. Phys. 76 (2006), 77–91] in which Hopf modules appearing as coefficients in Hopf-cyclic cohomology are interpreted as modules with flat connections. We start by descr...

We evaluate the sum of a finite group of linear characters of a Hopf algebra, at all grouplike and skew-primitive elements, and mention results for products of skew-primitive elements. Examples include quantum groups associated to semisimple and abelian Lie algebras, and degenerate affine Hecke algebras of reductive type with trivial parameter.

Abstract We show that if ${\mathcal C}$ is a fusion $2$ -category in which the endomorphism category of unit object or , then indecomposable objects form finite group.