In functional analysis, an abelian von Neumann algebra is a von Neumann algebra of operators on a Hilbert space in which all elements commute. The prototypical example of an abelian von Neumann algebra is the algebra L∞(X, μ) for μ a σ-finite measure on X realized as an algebra of operators on the Hilbert space L2(X, μ) as follows: Each f ∈ L∞(X, μ) is identified with the multiplication operator Of particular importance are the abelian von Neumann algebras on separable Hilbert spaces, particularly since they are completely classifiable by simple invariants. Though there is a theory for von Neumann algebras on non-separable Hilbert spaces (and indeed much of the general theory still holds in that case) the theory is considerably simpler for algebras on separable spaces and most applications to other areas of mathematics or physics only use separable Hilbert spaces. Note that if the measure spaces (X, μ) is a (that is X − N is a standard Borel space for some null set N and μ is a σ-finite measure) then L2(X, μ) is separable. (Wikipedia).

This is one of my all-time favorite differential equation videos!!! :D Here I'm actually using the Wronskian to actually find a nontrivial solution to a second-order differential equation. This is amazing because it brings the concept of the Wronskian back to life! And as they say, you won

From playlist Differential equations

Every Group of Order Five or Smaller is Abelian Proof

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Every Group of Order Five or Smaller is Abelian Proof. In this video we prove that if G is a group whose order is five or smaller, then G must be abelian.

From playlist Abstract Algebra

Differential Equations | Abel's Theorem

We present Abel's Theorem with a proof. http://www.michael-penn.net

From playlist Differential Equations

Abstract Algebra - 11.1 Fundamental Theorem of Finite Abelian Groups

We complete our study of Abstract Algebra in the topic of groups by studying the Fundamental Theorem of Finite Abelian Groups. This tells us that every finite abelian group is a direct product of cyclic groups of prime-power order. Video Chapters: Intro 0:00 Before the Fundamental Theorem

From playlist Abstract Algebra - Entire Course

Rigidity for von Neumann algebras – Adrian Ioana – ICM2018

Analysis and Operator Algebras Invited Lecture 8.5 Rigidity for von Neumann algebras Adrian Ioana Abstract: We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces.

From playlist Analysis & Operator Algebras

Jacob explains the fundamental concepts in group theory of what groups and subgroups are, and highlights a few examples of groups you may already know. Abelian groups are named in honor of Niels Henrik Abel (https://en.wikipedia.org/wiki/Niels_Henrik_Abel), who pioneered the subject of

From playlist Basics: Group Theory

8ECM Invited Lecture: Stuart White

From playlist 8ECM Invited Lectures

Kristin Courtney: "The abstract approach to classifying C*-algebras"

Actions of Tensor Categories on C*-algebras 2021 Mini Course: "The abstract approach to classifying C*-algebras" Kristin Courtney - Westfälische Wilhelms-Universität Münster Institute for Pure and Applied Mathematics, UCLA January 21, 2021 For more information: https://www.ipam.ucla.edu

From playlist Actions of Tensor Categories on C*-algebras 2021

Rolando de Santiago: "L2 cohomology and maximal rigid subalgebras of s-malleable deformations"

Actions of Tensor Categories on C*-algebras 2021 "L2 cohomology and maximal rigid subalgebras of s-malleable deformations" Rolando de Santiago - Purdue University, Department of Mathematics Abstract: A major theme in the study of von Neumann algebras is to investigate which structural as

From playlist Actions of Tensor Categories on C*-algebras 2021

Homomorphisms in abstract algebra

In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu

From playlist Abstract algebra

Jesse Peterson: Von Neumann algebras and lattices in higher-rank groups, Lecture 4

Mini course of the conference YMC*A, August 2021, University of Münster. Lecture 4: Von Neumann equivalence. Abstract: We’ll introduce measure equivalence (ME), W*-equivalence (W*E), and von Neumann equivalence (VNE). We’ll give examples and discuss invariants. YMC*A is an annual confere

From playlist YMC*A 2021

Jesse Peterson: Von Neumann algebras and lattices in higher-rank groups, Lecture 1

Mini course of the conference YMC*A, August 2021, University of Münster. Lecture 1: Background on von Neumann algebras. Abstract: We’ll briskly review basic properties of semi-finite von Neumann algebras. The standard representation, completely positive maps, group von Neumann algebras, th

From playlist YMC*A 2021

Lara Ismert: "Heisenberg Pairs on Hilbert C*-modules"

Actions of Tensor Categories on C*-algebras 2021 "Heisenberg Pairs on Hilbert C*-modules" Lara Ismert - Embry-Riddle Aeronautical University, Mathematics Abstract: Roughly speaking, a Heisenberg pair on a Hilbert space is a pair of self-adjoint operators (A,B) which satisfy the Heisenber

From playlist Actions of Tensor Categories on C*-algebras 2021

Damian Rössler: The arithmetic Riemann Roch Theorem and Bernoulli numbers

The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: (with V. Maillot) We shall show that integrality properties of the zero part of the abelian polylogarithm can be investigated using the arithme

From playlist HIM Lectures: Trimester Program "Periods in Number Theory, Algebraic Geometry and Physics"

Math 139 Fourier Analysis Lecture 31: Fourier Analysis on Finite Abelian Groups

Finite abelian groups; characters; dual group. Characters form an orthonormal family: cancellation property (moment condition) of characters; proof of orthonormality; the dual group is an orthonormal basis for the space of functions on the group. Linear algebra: spectral theorem (given a

From playlist Course 8: Fourier Analysis

Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - E.Effros

Edward Effros (UC Los Angeles) / 13.09.17 Title: Some remarkable gems and persistent difficulties in quantized functional analysis (QFA) Abstract: QFA was a direct outgrowth of the Heisenberg and von Neumann notions of quantized random variables. Thus, one replaces n-tuples of reals by c

From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

Pere Ara: Crossed products and the Atiyah problem

Talk by Pere Are in Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/crossed-products-and-the-atiyah-problem/ on March 19, 2021.

From playlist Global Noncommutative Geometry Seminar (Americas)

Kazuya Kato - Logarithmic abelian varieties

Correction: The affiliation of Lei Fu is Tsinghua University. This is a joint work with T. Kajiwara and C. Nakayama. Logarithmic abelian varieties are degenerate abelian varieties which live in the world of log geometry of Fontaine-Illusie. They have group structures which do not exist in

From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021

Christopher Schafhauser: "Non-stable extension theory and the classification of C∗-algebras"

Actions of Tensor Categories on C*-algebras 2021 "Non-stable extension theory and the classification of C∗-algebras" Christopher Schafhauser - University of Nebraska-Lincoln Abstract: Over the last decade, much of the progress in the classification and regularity theory of simple, nuclea

From playlist Actions of Tensor Categories on C*-algebras 2021