Generalised homomorphisms, measuring coalgebras and extended symmetries
Three categories of algebras with morphisms generalising the usual set of algebra homomorphisms are described. The Sweedler product provides a hom-tensor equivalence relating these three categories,…
AN INTRODUCTION TO TANNAKA DUALITY AND QUANTUM GROUPS
The goal of this paper is to give an account of classical Tannaka duality [C⁄] in such a way as to be accessible to the general mathematical reader, and to provide a key for entry to more recent…
Endomorphism Bialgebras of Diagrams and of Non-Commutative Algebras and Spaces
Bialgebras and Hopf algebras have a v ery complicated structure. It is not easy to construct explicit examples of such a n d c heck all the necessary properties. This gets even more complicated if we…
Reconstruction of Hidden Symmetries
Representations of a group $G$ in vector spaces over a field $K$ form a category. One can reconstruct the given group $G$ from its representations to vector spaces as the full group of monoidal…
Parachain Complexes and Yetter–Drinfeld Modules
In this article we show that the category of parachain complexes is equivalent to the category of Yetter–Drinfeld modules over the Pareigis's Hopf algebra.
Bialgebras Over Noncommutative Rings and a Structure Theorem for Hopf Bimodules
- MathematicsAppl. Categorical Struct.
A class of algebras whose module categories are also monoidal categories; however, the underlying functor to the category of k-vector spaces fails to be monoidal, it is shown that there is a suitable underlyingFunctor toThe category of B-bimodules over a k-algebra B which is monoidal with respect to the tensor product over B.
A quiver quantum group
We construct quantum groups at a root of unity and we describe their monoidal module category using techniques from the representation theory of finite dimensional associative algebras.
Universal Quantum (Semi)groups and Hopf Envelopes
- MathematicsAlgebras and Representation Theory
We prove that, in case $A(c)$ = the FRT construction of a braided vector space $(V,c)$ admits a weakly Frobenius algebra $\mathfrak B$ (e.g. if the braiding is rigid and its Nichols algebra is finite…
General representation theory in relatively closed monoidal categories
We apply the notion of relative adjoint functor to generalise closed monoidal categories. We define representations in such categories and give their relation with left actions of monoids. The…