Representations of non-commutative quantum groups

TL;DR

This paper explores the representation theory of a specific bialgebra linked to non-commutative quantum groups, providing new proofs and insights into Koszul algebras and their distributive properties.

Contribution

It offers a new proof regarding the distributivity of Koszul algebras and extends this property to certain N-Koszul algebras, advancing understanding in algebraic structures.

Findings

Koszul algebras are distributive

N-Koszul algebras can also be distributive

New proof techniques for algebraic properties

Abstract

We discuss the representation theory of the bialgebra end(A) introduced by Manin. As a side result we give a new proof that Koszul algebras are distributive and furthermore we show that some well-known N-Koszul algebras are also distributive.