2011/12/13 by Marat Aukhadiev, Aukhadiev, Marat Alfredovich
Mathematics · #16W30 #46L05 #46L65 #46L87 #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1112.2909
openalex publication_date 2011/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The generalization of multiplicative unitary notion from compact quantum groups to compact quantum semigroups is considered. We show why the same construction doesn't work in this case by giving examples of C*-algebras with non-trivial comultiplication which do not admit multiplicative unitaries. By the use of the pentagon equation we suggest a notion of an operator which gives comultiplication on any C*-algebra. The multiplicative unitary turns out to be its special case. We prove for some compact quantum semigroups that the comultiplication is given by such operator.