All bicovariant differential calculuses on GLq(3,C) and SLq(3,C)

DOI10.1088/0305-4470/28/9/015zbMATH Open0843.17019arXivhep-th/9411087OpenAlexW2068836555MaRDI QIDQ4847247

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Publication date: 11 September 1995

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Abstract: 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.

Full work available at URL: https://arxiv.org/abs/hep-th/9411087

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