Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces

Details Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces

1995-02-03

arxiv.org/abs/q-alg/9502005v1

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, Latex, no figures, to appear in the Proceedings of the XX International Conference on Group Theory Methods in Physic

Scientific paper

The vector fields of the quantum Lie algebra are described for the quantum groups $GL_q(N), SL_q(N)$ and $SO_q(N)$ as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms $SU_q(N)$ and $SO_q(N,R)$ are discussed in detail.

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