In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi
From playlist Algebra
The Lie-algebra of Quaternion algebras and their Lie-subalgebras
In this video we discuss the Lie-algebras of general quaternion algebras over general fields, especially as the Lie-algebra is naturally given for 2x2 representations. The video follows a longer video I previously did on quaternions, but this time I focus on the Lie-algebra operation. I st
From playlist Algebra
Lie groups: Poincare-Birkhoff-Witt theorem
This lecture is part of an online graduate course on Lie groups. We state the Poincare-Birkhoff Witt theorem, which shows that the universal enveloping algebra (UEA) of a Lie algebra is the same size as a polynomial algebra. We prove it for Lie algebras of Lie groups and sketch a proof of
From playlist Lie groups
This lecture is part of an online graduate course on Lie groups. We define the Lie algebra of a Lie group in two ways, and show that it satisfied the Jacobi identity. The we calculate the Lie algebras of a few Lie groups. For the other lectures in the course see https://www.youtube.co
From playlist Lie groups
This lecture is part of an online graduate course on Lie groups. This lecture is about Lie's theorem, which implies that a complex solvable Lie algebra is isomorphic to a subalgebra of the upper triangular matrices. . For the other lectures in the course see https://www.youtube.com/playl
From playlist Lie groups
Lie derivatives of differential forms
Introduces the lie derivative, and its action on differential forms. This is applied to symplectic geometry, with proof that the lie derivative of the symplectic form along a Hamiltonian vector field is zero. This is really an application of the wonderfully named "Cartan's magic formula"
From playlist Symplectic geometry and mechanics
Lie groups: Lie groups and Lie algebras
This lecture is part of an online graduate course on Lie groups. We discuss the relation between Lie groups and Lie algebras, and give several examples showing how they behave differently. Lie algebras turn out to correspond more closely to the simply connected Lie groups. We then explain
From playlist Lie groups
This lecture is part of an online graduate course on Lie groups. We give an introductory survey of Lie groups theory by describing some examples of Lie groups in low dimensions. Some recommended books: Lie algebras and Lie groups by Serre (anything by Serre is well worth reading) Repre
From playlist Lie groups
The Weyl algebra and the Heisenberg Lie algebra
In this video we give a simple teaser into the world of operator algebras. In particular, we talk about the Weyl algebra and compute some expressions that fulfill the property which defines the Heisenberg Lie algebra http://math.uchicago.edu/~may/REU2012/REUPapers/Lingle.pdf https://en.w
From playlist Algebra
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From playlist Be Smart - LATEST EPISODES!
Probability that a Person did Not Lie During a Polygraph Test
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Probability that a Person did Not Lie During a Polygraph Test
From playlist Statistics
NOTACON 6: The Strange and Creepy World of Brain Fingerprinting
Speaker: Ne0nRa1n Imagine a world in the future where your thoughts could be used against you to sentence you for a crime, could decide if you will be allowed fly on an airplane, or could decided whether or not your own government considers you a terrorist. Sound like something out of dys
From playlist Notacon 6
What's the difference between LAY and LIE? | Two Minute Grammar
Watch this video to know (in about 2 minutes) the difference between TO LAY and TO LIE (there are 2 verbs TO LIE in fact). These words that are often confused even by native English speakers. Improve your English grammar with this short videos series. Intermediate and advanced English le
From playlist 2 minute grammar
Can You Really Tell if Someone is Lying to You?
The internet is full of tips, tricks, and strategies to tell when somebody is lying, but the reality of lie detection isn't quite as clean and definitive as it is on TV. Hosted by: Hank Green ---------- Support SciShow by becoming a patron on Patreon: https://www.patreon.com/scishow -----
From playlist SciShow Psych
Toggler brain teaser | Puzzles | Math for fun and glory | Khan Academy
Separating the truthteller from the togglers! Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/math/math-for-fun-and-glory/puzzles/brain-teasers/v/alien-abduction-brain-teaser?utm_source=YT&utm_medium=Desc&utm_campaign=mathforfunandglory Missed the previous lesson?
From playlist Puzzles | Math for fun and glory | Khan Academy
Excel & Statistics 47: Empirical Rule (Bell Shaped Curve)
Download Excel Start File 1: https://people.highline.edu/mgirvin/AllClasses/210M/Content/ch03/Busn210ch03.xls Download Excel Finished File 1: https://people.highline.edu/mgirvin/AllClasses/210M/Content/ch03/Busn210ch03Finished.xls Download Excel Start File 2: https://people.highline.edu/mg
From playlist Excel 2007 Statistics: Charts, Functions, Formulas
Riddle For Genius - When Does The Thief Tell The Truth?
There's a short warm-up puzzle followed by the main puzzle. Thanks to Greg in Hungary (warm-up) and Jorn in Holland for suggesting these problems! *In my original video, I solved for day 3 with AND but mistakenly wrote "OR". Interestingly the OR is much easier to solve, and the answer wor
From playlist Logic Puzzles And Riddles
Riddle For Genius - When Does The Thief Tell The Truth?
A funny thing happened in this logic video. I solved a harder problem than was presented! It works out to the same answer, and usually it's a good thing in math to solve a stronger theorem. But in education it can be confusing. So I will make a revised video! Update, see the revised video:
From playlist Logic Puzzles And Riddles
Pavel Etingof: Poisson-Lie groups and Lie bialgebras - Lecture 3
HYBRID EVENT Recorded during the meeting "Lie Theory and Poisson Geometry" the January 12, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiov
From playlist Virtual Conference
Ulam's Game: Liar's Mathematics (#SoME2)
Ulam's game is an extension of the popular game 20 Questions, allowing the responding player to lie for one of their answers. Here we explore an intuitive approach to finding the optimal strategy for this new game. 0:00 Introduction 1:20 Defining the Problem 5:00 20 Questions 9:13 Ulam's
From playlist Summer of Math Exposition 2 videos