Classification of Bicovariant Differential Calculi

Details Classification of Bicovariant Differential Calculi Classification of Bicovariant Differential Calculi

1996-08-21

arxiv.org/abs/q-alg/9608016v2

Mathematics

Quantum Algebra

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

Scientific paper

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 $C G$ are also classified and shown to be in correspondence with pairs consisting of an irreducible representation $V$ and a continuous parameter in $C P^{dim V -1}$. They have dimension $dim V$. 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.

Affiliated with

Also associated with

No associations

Rating

Classification of Bicovariant Differential Calculi does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classification of Bicovariant Differential Calculi, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classification of Bicovariant Differential Calculi will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-162262