Classification of Bicovariant Differential Calculi

Abstract

We show that the bicovariant first order differential calculi on a factorisable semisimple quantum group are in 1-1 correspondence with irreducible representations $V$ of the quantum group enveloping algebra. The corresponding calculus is constructed and has dimension $dim{V}^2$. The differential calculi on a finite group algebra $CG$ are also classified and shown to be in correspondence with pairs consisting of an irreducible representation $V$ and a continuous parameter in $C{P}^{dimV-1}$. They have dimension $dimV$. For a classical Lie group we obtain an infinite family of non-standard calculi. General constructions for bicovariant calculi and their quantum tangent spaces are also obtained.

LATEX 25pp. no figs. Revised to clarify remarks re. Prop 2.5

References in corpus (1)

• Double-Bosonisation and the Construction of {$U_q(g)$}