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

1995/02/03 by Chong‐Sun Chu, Chong-Sun Chu, Bruno Zumino +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Covariant transformation #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Polynomial #Pseudodifferential operators #Pure mathematics #Quantum #Quantum Algebra (math.QA) #Quantum group #Quantum mechanics #Realization (probability) #Simple (philosophy) #hep-th #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9502005

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

arxiv created 1995/02/03 · openalex publication_date 1995/02/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Differential geometry on linear quantum groups

Cited by

• Quantum group covariant (anti)symmetrizers, -tensors, vielbein, Hodge map and Laplacian

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