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Derivations of Murray–von Neumann algebras

  • Aleksey Ber , Karimbergen Kudaybergenov ORCID logo EMAIL logo and Fedor Sukochev ORCID logo

Abstract

In this paper, we answer in the affirmative the long-standing conjecture that the first cohomology group of the Murray–von Neumann algebra S ( ) of all operators affiliated with a type II 1 von Neumann algebra is 0. That is, we show that all derivations of S ( ) are inner.

Acknowledgements

The authors thank J. Huang, G. Levitina and D. Zanin for detailed verification of the result presented in the present paper and useful comments concerning its exposition. We are indebted to the Referee for valuable suggestions and comments, which helped to improve our paper.

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Received: 2021-11-19
Revised: 2022-05-23
Published Online: 2022-08-10
Published in Print: 2022-10-01

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