Differential Calculi on the Quantum Group $SU_q(2)$ and Global $U(1)$-covariance

Details Differential Calculi on the Quantum Group $SU_q(2)$ and Global $U(1)$-covariance Differential Calculi on the Quantum Group $SU_q(2)$ and Global $U(1)$-covariance

1995-10-26

arxiv.org/abs/q-alg/9510025v1

Mathematics

Quantum Algebra

14 pages, latex

Scientific paper

A variety of three-dimensional left-covariant differential calculi on the quantum group $SU_q(2)$ is considered using an approach based on global $ U(1) $ -covariance. Explicit representations of possible $q $-Lie algebras are constructed in terms of differential operators. A gauge covariant differential algebra is uniquely determined. The non-standard Leibnitz rule is obtained for a corresponding $q$-Lie algebra.

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