The strong Morita equivalence for coactions of a finite dimensional C^*-Hopf algebra on unital C^*-algebras

2015/10/07 by Kazunori Kodaka, Kodaka, Kazunori, Tamotsu Teruya +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L05 #Secondary 46L08 #math.OA #msc:46L05 #msc:46L08

paper · pdf · doi:10.48550/arxiv.1510.01826

39 pages

arxiv created 2015/10/07 · openalex publication_date 2015/10/07 · arxiv updated 2015/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following Jansen and Waldmann, and Kajiwara and Watatani, we shall introduce notions of coactions of a finite dimensional C^*-Hopf algebra on a Hilbert C^*-bimodule of finite type in the sense of Kajiwara and Watatani and define their crossed product. We shall investigate their basic properties and show that the strong Morita equivalence for coactions preserves the Rohlin property for coactions of a finite dimensional C^*-Hopf algebra on unital C^*-algebras.

Related

• Coactions of a finite dimensional C^*-Hopf algebra on unital C^*-algebras, unital inclusions of unital C^*-algebras and the strong Morita equivalence
• Free coactions of a finite dimensional C^*-Hopf algebra and strong Morita equivalence
• The Rohlin property for coactions of finite dimensional C^*-Hopf algebras on unital C^*-algebras
• The generalized Picard groups for finite dimensional C^*-Hopf algebra coactions on unital C^*-algebras
• The strong Morita equivalence for inclusions of C^*-algebras and conditional expectations for equivalence bimodules