Hilbert Space Representations of Cross Product Algebras

2001/05/23 by Konrad Schmuedgen, Schmuedgen, Konrad, Elmar Wagner +1
Mathematics · #17B37 #47L55 #81R50 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:17B37 #msc:47L55 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/0105185

LaTeX2e, 44 pages; appears in Journal of Functional Analysis

openalex publication_date 2001/05/23 · arxiv created 2002/12/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hilbert space representations of cross product *-algebras of the Hopf *-algebras U_q(gl₂) with the coordinate algebras O(C²_q) and O(R³_q) of quantum vector spaces and U_q(su₂) with coordinate algebras O(SU_q(2)) and O(S²_q) of corresponding quantum spheres are investigated and classified. Invariant states on the coordinate *-algebras are described by two variants of the quantum trace.

Related

• Hilbert space representations of cross product algebras II
• Operator representations of cross product algebras of Podles' quantum spheres
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• Cross Product Quantisation, Nonabelian Cohomology And Twisting Of Hopf Algebras
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