“Quantum group” structure and “covariant” differential calculus on symmetric algebras corresponding to commutation factors on Z n

Abstract

Summary: ``For any given commutation factor ε on\bold Z\sp n a first order differential calculus on a certainsymmetric algebra \bold C\sb ε\sp n corresponding toε is constructed. It is shown that there exists a kindof quantum group structure (ε Hopf algebra) on each\bold C\sp n\sb ε and that the differential calculus isthe only one that is covariant (in an adapted sense) with respectto this `quantum group' structure.''\par {For the entirecollection see MR \Cite{Gielerak92:Quantum:Kluwer}[93h:00021].}