2003/05/27 by Klaus-Detlef Kuersten, Kuersten, Klaus-Detlef, Elmar Wagner +1
Mathematics · #17B37 #47L60 #81R50 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:17B37 #msc:47L60 #msc:81R50
paper · pdf · doi:10.48550/arxiv.math/0305380
35 pages
arxiv created 2003/05/27 · openalex publication_date 2003/05/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An operator theoretic approach to invariant integration theory on non-compact quantum spaces is introduced on the example of the quantum (n,1)-matrix ball Oq(Matn,1). In order to prove the existence of an invariant integral, operator algebras are associated to Oq(Matn,1) which allow an interpretation as ``rapidly decreasing'' functions and as functions with compact support on the quantum (n,1)-matrix ball. It is shown that the invariant integral is given by a generalization of the quantum trace. If an operator representation of a first order differential calculus over the quantum space is known, then it can be extended to the operator algebras of integrable functions. Hilbert space representations of Oq(Matn,1) are investigated and classified. Some topological aspects concerning Hilbert space representations are discussed.