Letters in Mathematical Physics

, Volume 22, Issue 3, pp 177-186

First online:

Differential calculus on quantized simple lie groups

  • Branislav JurčoAffiliated withDepartment of Optics, Palacký University

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Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q ∈ ℝ are also discussed.

AMS subject classifications (1991)

20N99 53C30 16S80