If N is a nilpotent operator on a finite-dimensional vector space, then there is a basis of the vector space with respect to which N has a matrix with only 0's on and below the diagonal.
From playlist Linear Algebra Done Right
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
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 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
This lecture is part of an online graduate course on Lie groups. We state Engel's theorem about nilpotent Lie algebras and sketch a proof of it. We give an example of a nilpotent Lie group that is not a matrix group. For the other lectures in the course see https://www.youtube.com/play
From playlist Lie groups
On the pioneering works of Professor I.B.S. Passi by Sugandha Maheshwari
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
Higgs bundles and higher Teichmüller components (Lecture 2) by Oscar García-Prada
DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif
From playlist Moduli Of Bundles And Related Structures 2020
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
Geometric deformations of orthogonal and symplectic Galois representations - Jeremy Booher
Jeremy Booher Stanford University November 19, 2015 https://www.math.ias.edu/seminars/abstract?event=87395 For a representation of the absolute Galois group of the rationals over a finite field of characteristic p, we would like to know if there exists a lift to characteristic zero with
From playlist Joint IAS/PU Number Theory Seminar
N J Wildberger Research Snapshot: Quantization and harmonic analysis on nilpotent Lie groups
A research snapshot of N JWildberger's PhD thesis.
From playlist Research Snapshots
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
Abstract Algebra | What is a ring?
We give the definition of a ring and present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Pre-recorded lecture 1: Introduction. What is Nijenhuis Geometry?
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
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
Nilpotent Ring Homomorphism (Abstract Algebra)
Nilpotent Ring Homomorphisms might not come up very often, but here is an example none the less. I hope you enjoy this problem and learn a thing or two. Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these lin
From playlist Abstract Algebra
Anthony Henderson: Hilbert Schemes Lecture 4
SMRI Seminar Series: 'Hilbert Schemes' Lecture 4 Kleinian singularities 1 Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested i
From playlist SMRI Course: Hilbert Schemes
Emily Cliff: Hilbert Schemes Lecture 3
SMRI Seminar Series: 'Hilbert Schemes' Lecture 3 The universal family on H Emily Cliff (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested in rep
From playlist SMRI Course: Hilbert Schemes
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