All bicovariant differential calculi on Glq(3,C) and SLq(3,C)
arXiv:hep-th/9411087 · doi:10.1088/0305-4470/28/9/015
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.
24 pages, LaTeX
References in corpus (9)
- Quantum group gauge theory on quantum spaces
- An introduction to non-commutative differential geometry on quantum groups
- Differential Geometry on Linear Quantum Groups
- An introduction to quantized Lie groups and algebras
- Quantum Group Gauge Theory on Classical Spaces
- Differential Calculus on Quantum Spaces and Quantum Groups
- Bicovariant differential geometry of the quantum group GL_q(3)
- Differential Calculi on Quantum (Sub-) Groups and Their Classical Limit
- The Differential Calculus on Quantum Linear Groups