Construction of a quantum Heisenberg group

2003/07/09 by Byung-Jay Kahng, Kahng, Byung-Jay
Mathematics · #46L65 #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:46L65

paper · pdf · doi:10.48550/arxiv.math/0307126

22 pages

openalex publication_date 2003/07/09 · arxiv created 2004/05/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a construction of a (C*-algebraic) quantum Heisenberg group. This is done by viewing it as the dual quantum group of the specific non-compact quantum group (A,Δ) constructed earlier by the author. Our definition of the quantum Heisenberg group is different from the one considered earlier by Van Daele. To establish our object of study as a locally compact quantum group, we also give a discussion on its Haar weight, which is no longer a trace. In the latter part of the paper, we give some additional discussion on the duality mentioned above.

Citations

• KMS-weights on C*-algebras

Related

• Quantum double construction in the C*-algebra setting of certain Heisenberg-type quantum groups
• Locally compact quantum groups in the von Neumann algebraic setting
• Universal C*-algebraic quantum groups arising from algebraic quantum groups
• Haar measure on a locally compact quantum group
• *-Representations of a Quantum Heisenberg Group Algebra