# A non-commutative non-cocommutative Hopf algebra in “nature”

```@article{Pareigis1981ANN,
title={A non-commutative non-cocommutative Hopf algebra in “nature”},
author={Bodo Pareigis},
journal={Journal of Algebra},
year={1981},
volume={70},
pages={356-374}
}```
65 Citations
Generalised homomorphisms, measuring coalgebras and extended symmetries
• Mathematics
• 2021
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
• Mathematics
• 1991
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
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
• M. Farinati
• Mathematics
Algebras and Representation Theory
• 2022
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
Cauchy completeness for DG-categories
• Mathematics
• 2020
We go back to the roots of enriched category theory and study categories enriched in chain complexes; that is, we deal with differential graded categories (DG-categories for short). In particular, we