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

Source: [All bicovariant differential calculi on Glq(3,C) and SLq(3,C)](<https://www.sota2.com/research/paper/68fa242d2c2a3760193a0425>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T08:34:39.843Z

Authors: K. Bresser

Published: 1994-11-12T19:09:32.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-th/9411087>)

[PDF](<https://arxiv.org/pdf/hep-th/9411087.pdf>)