## Journal of the Mathematical Society of Japan

### On commuting canonical endomorphisms of subfactors

Takashi SANO

#### Abstract

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 $\mathrm{co}$-commuting square condition and the existence of two simultaneous commuting canonical endomorphisms is discussed.

#### Article information

Source
J. Math. Soc. Japan, Volume 55, Number 1 (2003), 131-142.

Dates
First available in Project Euclid: 5 December 2007

https://projecteuclid.org/euclid.jmsj/1196890846

Digital Object Identifier
doi:10.2969/jmsj/1196890846

Mathematical Reviews number (MathSciNet)
MR1939189

Zentralblatt MATH identifier
1027.46081

Subjects
Primary: 46L37: Subfactors and their classification

#### Citation

SANO, Takashi. On commuting canonical endomorphisms of subfactors. J. Math. Soc. Japan 55 (2003), no. 1, 131--142. doi:10.2969/jmsj/1196890846. https://projecteuclid.org/euclid.jmsj/1196890846