2024/01/03 by Keshab Chandra Bakshi, Satyajit Guin, Bakshi, Keshab Chandra +2 · 2 citations
Engineering · Mathematics · #37A35 #46L10 #46L37 #46L55 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2401.01664
openalex publication_date 2024/01/03 · openalex created_date 2024/01/05 · openalex updated_date 2026/07/28
We show that any two Hadamard subfactors arising from a pair of distinct complex Hadamard matrices of order 3 are either equal or conjugate by a unitary in the relative commutant of their intersection. Moreover, when the Hadamard subfactors are not equal, we prove the factoriality of their intersection, and it turns out to be a vertex model subfactor. We compute the first relative commutant and characterize this subfactor by identifying it with a particular type of Krishnan-Sunder subfactor. A few key invariants, including the Pimsner-Popa probabilistic number, the angle, and the Connes-Størmer relative entropy for the pair of Hadamard subfactors are computed to understand their relative position.