A differential calculus on the quantum group $SU_q(2)$ compatible with the gauge-transformation structure

D. G. Pak

V. I. Lenin Tashkent State University

Abstract: We consider a three-dimensional bicovariant differential calculus on the quantum group $SU_q(2)$ that is compatible with the structure of gauge transformations. In the approach based on the global covariance with respect to the stability subgroup $U(1)$, we show that the gauge-covariant exterior differential algebra on $SU_q(2)$ is uniquely determined. We construct explicit representations of $q$-deformed Lie algebras in terms of differential operators.

Received: 24.12.1997
Revised: 18.03.1998

DOI: 10.4213/tmf902

 English version: Theoretical and Mathematical Physics, 1998, 116:2, 947–955

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