相关论文: Set theory and von Neumann algebras

Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.

We present a self-contained analysis of infinity from two mathematical perspectives: set theory and algebra. We begin with cardinal and ordinal numbers, examining deep questions such as the continuum hypothesis, along with foundational…

This document comprises Level Theory, parts 1-3. PART 1. The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any sets…

A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on…

These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…

Those notes rest on the Samuel Eilenberg Lectures I gave at Columbia University, NY, in the fall 2022. I thank all the mathematicians who participated in their elaboration, directly or indirectly. They are meant to be published as a…

These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.

We explore an application of homological algebra to set theoretic objects by developing a cohomology theory for Hausdorff gaps. The cohomology theory is introduced with enough generality to be applicable to other questions in set theory.…

Several letters by Kurt G\"odel and Johann (J\'anos) von Neumann from the (so far uncatalogued) archive of Abraham (Adolf) Fraenkel at the National Library of Israel are published and discussed. These include two fragments by G\"odel of…

These are the lecture notes for the LMS/EPSRC short course on strong approximation methods in linear groups organized by Dan Segal in Oxford in September 2007.

The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…

This is a survey article on some connections between cluster algebras and link invariants, written for the Notices of the AMS.

This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.

Results concerning recurrence and ergodicity are proved in an abstract Hilbert space setting based on the proof of Khintchine's recurrence theorem for sets, and on the Hilbert space characterization of ergodicity. These results are carried…

These lecture notes were prepared as a basic introduction to the theory of constrained systems which is how the fundamental forces of nature appear in their Hamiltonian formulation. Only a working knowledge of Lagrangian and Hamiltonian…

We extend Ueda's peak set theorem for subdiagonal subalgebras of tracial finite von Neumann algebras, to sigma-finite von Neumann algebras (that is, von Neumann algebras with a faithful state; which includes those on a separable Hilbert…

These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological…

These are Notes prepared for nine lectures given at the Mathematical Sciences Research Institute, MSRI, Berkeley during the period January--March 1995. It is a pleasant duty to record here my gratitude to MSRI, and its staff, for making…

We study the Lie algebra structure of the Onsager algebra from the ideal theoretic point of view. A structure theorem of ideals in the Onsager algebra is obtained with the connection to the finite-dimensional representations. We also…

We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…