Open Access
January, 2003 On commuting canonical endomorphisms of subfactors
Takashi SANO
J. Math. Soc. Japan 55(1): 131-142 (January, 2003). DOI: 10.2969/jmsj/1196890846


In the Jones Index theory, Longo's sector theory has been a powerful approach to the analysis for inclusions of factors and canonical endomorphisms have played an important role. In this paper, two topics on commuting canonical endomorphisms are studied: For a composition of two irreducible inclusions of depth 2 factors, the commutativity of corresponding canonical endomorphisms is shown to be the condition for the ambient irreducible inclusion to be of depth 2, that is, to give a finite dimensional Kac algebra. And an equivalent relation between the commuting co-commuting square condition and the existence of two simultaneous commuting canonical endomorphisms is discussed.


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Takashi SANO. "On commuting canonical endomorphisms of subfactors." J. Math. Soc. Japan 55 (1) 131 - 142, January, 2003.


Published: January, 2003
First available in Project Euclid: 5 December 2007

zbMATH: 1027.46081
MathSciNet: MR1939189
Digital Object Identifier: 10.2969/jmsj/1196890846

Primary: 46L37

Keywords: canonical endomorphism , commuting square , depth 2 inclusion , Kac Algebra

Rights: Copyright © 2003 Mathematical Society of Japan

Vol.55 • No. 1 • January, 2003
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