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Differential calculus on quantized simple Lie groups. (English) Zbl 0753.17020

The author introduces a generalization of S. L. Woronowicz’s [Commun. Math. Phys. 122, 125-170 (1989; Zbl 0751.58042)] four dimensional differential calculus on \(SU_ q(2)\) to the case of an arbitrary simple classical quantum group in a constructive way.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
46L87 Noncommutative differential geometry
46L85 Noncommutative topology

Citations:

Zbl 0751.58042
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References:

[1] Woronowicz, S. L., Differential calculus on compact matrix pseudogroups (quantum groups), Comm. Math. Phys. 122, 125–170 (1989). · Zbl 0751.58042 · doi:10.1007/BF01221411
[2] Woronowicz, S. L., Twisted SU(2) group. An example of noncommutative differential calculus, Publ. RIMS, Kyoto University 23, 117–181 (1987). · Zbl 0676.46050 · doi:10.2977/prims/1195176848
[3] Podleś, P. and Woronowicz, S. L., Quantum deformation of Lorentz group, Mittag-Leffler Inst. Report No. 20, 1988/89.
[4] Podleś, P., Differential calculus on quantum spheres, Lett. Math. Phys. 18, 107–119 (1989). · Zbl 0702.53073 · doi:10.1007/BF00401865
[5] Reshetikhin, N. Yu., Takhtajan, L. A., and Faddeev, L. D., Quantization of Lie groups and Lie algebras (in Russian), Algebra i analiz 1, 178–206 (1989).
[6] Jimbo, M., A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10, 63–69 (1985); Jimbo, M., A q-analogue of U(gl(N+1)), Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11, 247–252 (1986). · Zbl 0587.17004 · doi:10.1007/BF00704588
[7] Drinfel’d, V. G., Quantum groups, in Proc. Intl. Cong. of Math. 1986, p. 798.
[8] Woronowicz, S. L., Compact matrix pseudogroups, Comm. Math. Phys. 111, 613–655 (1987). · Zbl 0627.58034 · doi:10.1007/BF01219077
[9] Burroughs, N., Relating the approaches to quantised algebras and quantum groups, DAMPT preprint DAMPT/R-89/11. · Zbl 0721.17016
[10] Moore, G. and Reshetikhin, N. Yu., A comment on quantum group symmetry in conformal field theory, IRS preprint IRSSNS-HEP-89/18.
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