2000/12/30 by Malgorzata Rowicka-Kudlicka, Małgorzata Rowicka-Kudlicka, Rowicka-Kudlicka, Malgorzata
Mathematics · Physics and Astronomy · #20G42 #47B25 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:20G42 #msc:47B25
paper · pdf · doi:10.48550/arxiv.math/0101003
31 pages LaTeX, no figures
openalex publication_date 2000/12/30 · arxiv created 2001/01/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider quantum group theory on the Hilbert space level. We find all unitary representations of three braided quantum groups related to the quantum ``ax+b'' group. First we introduce an auxiliary braided quantum group, which is apparently not related to the quantum ``ax+b'' group, but easy to work with. We find all unitary representations of this quantum group. Then we use this result to find all unitary representations of another braided quantum group, whose C*-algebra is generated by two (out of three) generators generating (in the sense of Woronowicz) C*-algebra of the quantum ``ax+b''- group. We find all unitary representations of this other braided quantum group. This is the most difficult result needed to classify all unitary representations of the quantum ``ax+b'' group.