In algebra, the bicommutant of a subset S of a semigroup (such as an algebra or a group) is the commutant of the commutant of that subset. It is also known as the double commutant or second commutant and is written . The bicommutant is particularly useful in operator theory, due to the von Neumann double commutant theorem, which relates the algebraic and analytic structures of operator algebras. Specifically, it shows that if M is a unital, self-adjoint operator algebra in the C*-algebra B(H), for some Hilbert space H, then the weak closure, strong closure and bicommutant of M are equal. This tells us that a unital C*-subalgebra M of B(H) is a von Neumann algebra if, and only if, , and that if not, the von Neumann algebra it generates is . The bicommutant of S always contains S. So . On the other hand, . So , i.e. the commutant of the bicommutant of S is equal to the commutant of S. By induction, we have: and for n > 1. It is clear that, if S1 and S2 are subsets of a semigroup, If it is assumed that and (this is the case, for instance, for von Neumann algebras), then the above equality gives (Wikipedia).
David Penneys: Bicommutant categories from multifusion categories
David Penneys: Bicommutant categories from (multi)fusion categories Abstract: I'll discuss an ongoing joint project with Andre Henriques. Just as a tensor category is a categorification of a ring, and its Drinfeld center is a categorification of the center of a ring, a bicommutant categor
From playlist HIM Lectures: Trimester Program "Von Neumann Algebras"
Rahul Savani: Polymatrix Games Algorithms and Applications
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From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"
What is a Bipartite Graph? | Graph Theory
What is a bipartite graph? We go over it in today’s lesson! I find all of these different types of graphs very interesting, so I hope you will enjoy this lesson. A bipartite graph is any graph whose vertex set can be partitioned into two disjoint sets (called partite sets), such that all e
From playlist Graph Theory
Adding Vectors Geometrically: Dynamic Illustration
Link: https://www.geogebra.org/m/tsBer5An
From playlist Trigonometry: Dynamic Interactives!
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► My Trigonometry course: https://www.kristakingmath.com/trigonometry-course Trig identities are pretty tough for most people, because 1) there are so many of them, and 2) they’re hard to remember, and 3) it’s tough to recognize when you’re supposed to use them! But don’t worry, because
From playlist Trigonometry
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Link: https://www.geogebra.org/m/cuCwguXP BGM: Simeon Smith
From playlist Trigonometry: Dynamic Interactives!
Arthur Troupel - Free Wreath Products as Fundamental Graph C*-algebras
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From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”
Learn how to eliminate the parameter with trig functions
Learn how to eliminate the parameter in a parametric equation. A parametric equation is a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters. Eliminating the parameter allows us to write parametric equation in r
From playlist Parametric Equations
Trigonometry & Bearings (2 Bearings): Dynamic & Modifiable Illustrator
Link: https://www.geogebra.org/m/nXNFgdvf BGM: Edward Shearmur
From playlist Trigonometry: Dynamic Interactives!
In this video I remind you of the derivatives of a few transcendental functions such as exponent x and the trigonometric functions.
From playlist Biomathematics
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Links: https://www.geogebra.org/m/dj8jwyNV https://www.geogebra.org/m/QNJMwctd BGM: Edward Shearmur
From playlist Trigonometry: Dynamic Interactives!
Francesc Fité, Sato-Tate groups of abelian varieties of dimension up to 3
VaNTAGe seminar on April 7, 2020 License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Jesse Peterson: Von Neumann algebras and lattices in higher-rank groups, Lecture 1
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From playlist YMC*A 2021
Use even and odd functions to evaluate trigonometric functions
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From playlist Simplify Trig Functions Using Identities