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**Von Neumann algebras in mathematics and physics.**
*(English)*
Zbl 1356.46001

Cheng, Shiu-Yuen (ed.) et al., Introduction to modern mathematics. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-305-0/pbk). Advanced Lectures in Mathematics (ALM) 33, 285-321 (2015).

Summary: These are the notes for the Chern lectures that I gave at Tsinghua University in late December 2012. The notes were prepared in haste as I was preparing the lectures. As such everything in them must be regarded with suspicion – all definitions are incomplete, all theorems are wrong as stated and attributions are likely to be misleading. I have tried to include enough references to the literature for the interested readers to track down the truth, while trying to retain some readabilty to reflect the somewhat informal nature of the talks. I apologise to any mathematicians or physicists whose work is not given the correct recognition. It is also true of course that the choice and emphasis of topics is largely influenced by my own work. The story told by another worker in von Neumann algebras would not doubt be completely different.

For the entire collection see [Zbl 1326.00080].

For the entire collection see [Zbl 1326.00080].

### MSC:

46-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis |

46L10 | General theory of von Neumann algebras |

46L37 | Subfactors and their classification |

46L54 | Free probability and free operator algebras |

46L60 | Applications of selfadjoint operator algebras to physics |

57M25 | Knots and links in the \(3\)-sphere (MSC2010) |

81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |