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

Chong-Sun Chu; Bruno Zumino

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

q-alg 2008-02-03 v1 High Energy Physics - Theory Quantum Algebra

Authors: Chong-Sun Chu , Bruno Zumino

Abstract

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.

Keywords

quantum groups quantum group representations pseudodifferential operators

Cite

@article{arxiv.q-alg/9502005,
  title  = {Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces},
  author = {Chong-Sun Chu and Bruno Zumino},
  journal= {arXiv preprint arXiv:q-alg/9502005},
  year   = {2008}
}

Comments

16 pages, Latex, no figures, to appear in the Proceedings of the XX International Conference on Group Theory Methods in Physics, Toyonaka, Japan (1994)

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

Abstract

Keywords

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