In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra of a Lie algebra that is self-normalising (if for all , then ). They were introduced by Élie Cartan in his doctoral thesis. It controls the representation theory of a semi-simple Lie algebra over a field of characteristic . In a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero (e.g., ), a Cartan subalgebra is the same thing as a maximal abelian subalgebra consisting of elements x such that the adjoint endomorphism is semisimple (i.e., diagonalizable). Sometimes this characterization is simply taken as the definition of a Cartan subalgebra.pg 231 In general, a subalgebra is called toral if it consists of semisimple elements. Over an algebraically closed field, a toral subalgebra is automatically abelian. Thus, over an algebraically closed field of characteristic zero, a Cartan subalgebra can also be defined as a maximal toral subalgebra. Kac–Moody algebras and generalized Kac–Moody algebras also have subalgebras that play the same role as the Cartan subalgebras of semisimple Lie algebras (over a field of characteristic zero). (Wikipedia).
CAS GeoGebra: Resolviendo ecuaciones cuadráticas (básico)
Utilizando la aplicación CAS de Geogebra podemos resolver fácilmente ecuaciones como las polinómicas de segundo grado. En el video se muestran algunos ejemplos.
From playlist GeoGebra para celulares
Xin Li: Cartan subalgebras in C*-algebras
This talk is about the notion of Cartan subalgebras introduced by Renault, based on work of Kumjian. We explain how Cartan algebras build a bridge between dynamical systems and operator algebras, and why this notion might be interesting for the structure theory of C*-algebras as well. The
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
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From playlist GeoGebra Geometry
Resolviendo sistemas de ecuaciones en GeoGebra
A partir de ejemplos veremos como resolver sistemas de ecuaciones en GeoGebra utilizando la vista algebraica CAS
From playlist GeoGebra - Vista CAS
Stefaan Vaes - Classification of regular subalgebras of the hyperfinite II1 factor
I present a joint work with Sorin Popa and Dimitri Shlyakhtenko. We prove that under a natural condition, the regular von Neumann subalgebras B of the hyperfinite II1 factor R are completely classified (up to conjugacy by an automorphism of R) by the associated discrete measured groupoid.
From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
Ingresar una matriz en la app de GeoGebra
Ingreso de una matriz para obtener su inversa en la aplicación Calculadora gráfica de GeoGebra
From playlist GeoGebra para celulares
Representations of Galois algebras – Vyacheslav Futorny – ICM2018
Lie Theory and Generalizations Invited Lecture 7.3 Representations of Galois algebras Vyacheslav Futorny Abstract: Galois algebras allow an effective study of their representations based on the invariant skew group structure. We will survey their theory including recent results on Gelfan
From playlist Lie Theory and Generalizations
Octahedron in Geogebra Step by step tutorial here: https://youtu.be/LmCs6dzZreA In case you wanna to pay me a drink: https://www.paypal.me/admirsuljicic/
From playlist Geogebra [Tutoriali]
Stefaan Vaes: Cohomology and L2-Betti numbers for subfactors and quasi-regular inclusions
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Analysis and its Applications
Inversa de una matriz - GeoGebra app
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From playlist GeoGebra para celulares
Kevin Buzzard (lecture 18/20) Automorphic Forms And The Langlands Program [2017]
Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w
From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]
What Morse missed by not talking to Weyl - Raoul Bott
75th Anniversary Celebration School of Mathematics Raoul Bott Harvard University March 12, 2005 More videos on http://video.ias.edu
From playlist Mathematics
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From playlist Mathematics
Explicitly characterizing a Casimir Element of a Five Dimensional Representation of a Uq (SP4)
Speakers; M.Krawczyk (Defining Lie Algebra & the Representations of Lie Algebras). Z.Davis(Weight Spaces, Root systems, Lemma(via Kuan), The Central Element, 5-dimensional Fundamental Representation, Pairing & Dual Basis). R.Campbell(Cartan subalgebras, Quantization, Universal Enveloping
From playlist 2017 Summer REU Presentations
FUNGSI KUADRAT DENGAN GEOGEBRA
Video ini mencoba menggambar grafik fungsi kuadrat dengan geogebra. Tutorial geogebra menggambar grafik fungsi kuadrat seperti titik maksimum, akar-akar persamaan kuadrat, deksriminan dan sumbu simetri. Semoga bermanfaat.. Penulis juga telah menerbitkan buku tutorial geogebra https://bit.
From playlist Geogebra Videos
Anton Alekseev: Poisson-Lie duality and Langlands duality via Bohr-Sommerfeld
Abstract: Let G be a connected semisimple Lie group with Lie algebra 𝔤. There are two natural duality constructions that assign to it the Langlands dual group G^∨ (associated to the dual root system) and the Poisson-Lie dual group G^∗. Cartan subalgebras of 𝔤^∨ and 𝔤^∗ are isomorphic to ea
From playlist Topology
On the crossroads of enumerative geometry and representation theory – Andrei Okounkov – ICM2018
Plenary Lecture 4 On the crossroads of enumerative geometry and geometric representation theory Andrei Okounkov Abstract: The subjects in the title are interwoven in many different and very deep ways. I recently wrote several expository accounts that reflect a certain range of developmen
From playlist Plenary Lectures
Misterios del agua de las fuentes.
Aprende sobre la reflexión y refracción de la luz a través de los misterios del agua de las fuentes comunes y corrientes.
From playlist Exploratorium | Español