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March 12, 2021 By

A Remark on the Functoriality of the Connes-Takesaki Flow of Weights

C. R. Math. Rep. Acad. Sci. Canada Vol. 43 (1) 2021, pp. 28-44

March 31, 2021

George A. Elliott, Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4; e-mail: elliott@math.toronto.edu

Abstract/Résumé:

The flow of weights was introduced by Connes and Takesaki as a functor on the category of von Neumann algebras with isomorphisms as maps. While it is easy to see that this functor cannot be extended to the category of all von Neumann algebra homomorphisms, it is in fact possible to extend it to a certain extent. This can also be done, fairly extensively, for the Falcone and Takesaki non-commutative flow of weights.

Le flot des poids a été introduit par Connes et Takesaki comme foncteur sur la catégorie des algèbres de von Neumann avec isomorphismes comme flèches. On peut étendre ce foncteur jusqu’à un certain point dans les directions et covariante et contravariante. Le foncteur flot des poids non-commutatif peut aussi s’étendre, bien entendant pas aux homomorphismes arbitraires.

Keywords: Connes-Takesaki flow of weights, functoriality, non-commutative flow of weights
AMS Subject Classification: , Categories; functors 46L36, 46M15

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