Representations at a Root of Unity of q-Oscillators and Quantum Kac-Moody algebras

1994/09/14 by Jens-U. H. Petersen, Petersen, Jens-U. H.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.hep-th/9409079

openalex publication_date 1994/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here is a list of chapters: 1 Introduction 2 Notation and preliminaries Part I: Finite quantum groups 3 2x2 Matrix quantum groups and the quantum plane 4 Quantum enveloping algebras at a root of unity Part II: q-Oscillators 5 Representations of q-oscillators at a root of unity 6 qr-Oscillator at a root of unity Part III: Infinite quantum groups 7 Quantum affine algebras 8 Quantum affine algebras at a root of unity

Citations

• Free field realization of q-deformed primary fields for U_q(\widehat\sl₂)
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Q-analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum enveloping algebras

Related

• Quantum Groups,Deformed Oscillators and their Interrelations
• Quantum "az+b" group at roots of unity: unitary representations
• Quantum algebras and Lie groups
• Some introductory notes on quantum groups, quantum algebras, and their applications
• Introduction to Quantum Algebras