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
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
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
Lie Groups and Lie Algebras: Lesson 25 - the commutator and the Lie Algebra
Lie Groups and Lie Algebras: Lesson 25 - the commutator In this lecture we discover how to represent an infinitesimal commutator of the Lie group using a member of the Lie algebra. We promote the vector space spawned by the group generators to an algebra. Please consider supporting this
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 18- Group Generators
Lie Groups and Lie Algebras: Lesson 18- Generators This is an important lecture! We work through the calculus of *group generators* and walk step-by-step through the exploitation of analyticity. That is, we use the Taylor expansion of the continuous functions associated with a Lie group o
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 16 - representations, connectedness, definition of Lie Group
Lie Groups and Lie Algebras: Lesson 16 - representations, connectedness, definition of Lie Group We cover a few concepts in this lecture: 1) we introduce the idea of a matrix representation using our super-simple example of a continuous group, 2) we discuss "connectedness" and explain tha
From playlist Lie Groups and Lie Algebras
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
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
Geometric Algebra - The Matrix Representation of a Linear Transformation
In this video, we will show how matrices as computational tools may conveniently represent the action of a linear transformation upon a given basis. We will prove that conventional matrix operations, particularly matrix multiplication, conform to the composition of linear transformations.
From playlist Geometric Algebra
Representations of p-adic groupsz - Jessica Fintzen
Workshop on Representation Theory and Analysis on Locally Symmetric Spaces Topic: Representations of p-adic groupsz Speaker: Jessica Fintzen Affiliation: University of Michigan; Member, School of Mathematics Date: March 5, 2018 For more videos, please visit http://video.ias.edu
From playlist Representation Theory and Analysis on Locally Symmetric Spaces WS
David Zywina, Computing Sato-Tate and monodromy groups.
VaNTAGe seminar on May 5, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
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
Lie Groups and Lie Algebras: Lesson 41: Elementary Representation Theory I
Lie Groups and Lie Algebras: Lesson 41: Elementary Representation Theory I I wanted to begin a more intricate example of the principle of a Universal Covering group, but I think I need to cover a little background material. We need to get a grip on what is meant by "Representation Theory"
From playlist Lie Groups and Lie Algebras
Representation theory and geometry – Geordie Williamson – ICM2018
Plenary Lecture 17 Representation theory and geometry Geordie Williamson Abstract: One of the most fundamental questions in representation theory asks for a description of the simple representations. I will give an introduction to this problem with an emphasis on the representation theor
From playlist Plenary Lectures
Moduli of p-divisible groups (Lecture 4) by Ehud De Shalit
PROGRAM PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France
From playlist Perfectoid Spaces 2019
Lars Thorge Jensen: Cellularity of the p-Kazhdan-Lusztig Basis for Symmetric Groups
After recalling the most important results about Kazhdan-Lusztig cells for symmetric groups, I will introduce the p-Kazhdan-Lusztig basis and give a complete description of p-cells for symmetric groups. After that I will mention important consequences of the Perron-Frobenius theorem for p-
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Nigel Higson: Real reductive groups, K-theory and the Oka principle
The lecture was held within the framework of Follow-up Workshop TP Rigidity. 29.4.2015
From playlist HIM Lectures 2015
Lie Groups and Lie Algebras: Lesson 7 - The Classical Groups Part V
Lie Groups and Lie Algebras: Lesson 7 - The Classical Groups Part V We discuss the matrix interpretation of the metric even more, since it is critical to our understanding of the classical groups. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras