Differential geometry on linear quantum groups

1992/06/01 by Peter Schupp, Paul Watts, Bruno Zumino · 6 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #hep-th #math.QA

paper · pdf · doi:10.1007/bf00398310

published as Lett.Math.Phys. 25 (1992) 139-148 · 15 pages

openalex publication_date 1992/06/01 · arxiv created 1992/07/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An exterior derivative, inner derivation, and Lie derivative are introduced on the quantum group GL_q(N). SL_q(N) is then found by constructing matrices with determinant unity, and the induced calculus is found.

Citations

• Differential calculus on compact matrix pseudogroups (quantum groups)
• Multiparametric quantum deformation of the general linear supergroup

Cited by

• GLq(N)-covariant quantum algebras and covariant differential calculus
• The Weyl approach to the representation theory of reflection equation algebra
• Non-Abelian phenomena on D-branes
• Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces
• Spectral Extension of the Quantum Group Cotangent Bundle
• Standard complex for quantum Lie algebras