Simple Lie group

Lie groups: Lie algebras

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

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

Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined

Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined In this lecture we define a "continuous groups" and show the connection between the algebraic properties of a group with topological properties. Please consider supporting this channel via Patreon: https://www.patreon.co

From playlist Lie Groups and Lie Algebras

Simple groups, Lie groups, and the search for symmetry II | Math History | NJ Wildberger

This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry. During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in describing symmetry in geometry. In this video we talk abou

From playlist MathHistory: A course in the History of Mathematics

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

Lie groups: Positive characteristic is weird

This lecture is part of an online graduate course on Lie groups. We give several examples to show that, over fields of positive characteristic, Lie algebras can behave strangely, and have a weaker connection to Lie groups. In particular the Lie algebra does not generate the ring of all in

From playlist Lie groups

Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators

Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators A Lie group can always be considered as a group of transformations because any group can transform itself! In this lecture we replace the "geometric space" with the Lie group itself to create a new collection of generators. P

From playlist Lie Groups and Lie Algebras

Lie groups: Introduction

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

Lie Groups and Lie Algebras: Lesson 3 - Classical Groups Part I

Lie Groups and Lie Algebras: Lesson 3 - Classical Groups Part I We introduce the idea of the classical matrix groups and their associated carrier spaces. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX

From playlist Lie Groups and Lie Algebras

Simple Groups - Abstract Algebra

Simple groups are the building blocks of finite groups. After decades of hard work, mathematicians have finally classified all finite simple groups. Today we talk about why simple groups are so important, and then cover the four main classes of simple groups: cyclic groups of prime order

From playlist Abstract Algebra

Jean Michel BISMUT - Fokker-Planck Operators and the Center of the Enveloping Algebra

The heat equation method in index theory gives an explicit local formula for the index of a Dirac operator. Its Lagrangian counterpart involves supersymmetric path integrals. Similar methods can be developed to give a geometric formula for semi simple orbital integrals associated with the

From playlist Integrability, Anomalies and Quantum Field Theory

Ana Balibanu: The partial compactification of the universal centralizer

Abstract: Let G be a semisimple algebraic group of adjoint type. The universal centralizer is the family of centralizers in G of regular elements in Lie(G), parametrized by their conjugacy classes. It has a natural symplectic structure, obtained by Hamiltonian reduction from the cotangent

From playlist 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

Lie groups: Lie's theorem

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

Simple grps 1 by N. S. Narasimha Sastry

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Simple groups, Lie groups, and the search for symmetry I | Math History | NJ Wildberger

During the 19th century, group theory shifted from its origins in number theory and the theory of equations to describing symmetry in geometry. In this video we talk about the history of the search for simple groups, the role of symmetry in tesselations, both Euclidean, spherical and hyper

From playlist MathHistory: A course in the History of Mathematics