All bicovariant differential calculi on Glq(3,C) and SLq(3,C)

Details All bicovariant differential calculi on Glq(3,C) and SLq(3,C) All bicovariant differential calculi on Glq(3,C) and SLq(3,C)

1994-11-12

arxiv.org/abs/hep-th/9411087v1

J.Phys. A28 (1995) 2545-2562

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, LaTeX

Scientific paper

10.1088/0305-4470/28/9/015

All bicovariant first order differential calculi on the quantum group GLq(3,C) are determined. There are two distinct one-parameter families of calculi. In terms of a suitable basis of 1-forms the commutation relations can be expressed with the help of the R-matrix of GLq(3,C). Some calculi induce bicovariant differential calculi on SLq(3,C) and on real forms of GLq(3,C). For generic deformation parameter q there are six calculi on SLq(3,C), on SUq(3) there are only two. The classical limit q-->1 of bicovariant calculi on SLq(3,C) is not the ordinary calculus on SL(3,C). One obtains a deformation of it which involves the Cartan-Killing metric.

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