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
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 derivative of a vector field (flow and pushforward)
Part 2: https://youtu.be/roFNj3k4Lmc In this video I show you how you can derive the Lie derivative of a vector field. First, we look at a vector field on a manifold and develop the notion of an integral curve followed by the flow of the vector field. We can then move another vector along
From playlist Lie derivative
In this clip I casually give a roundup of some of my current interests and also recommend you some literature. Get into Lie algebras, Lie groups and algebraic groups. Do it now! https://en.wikipedia.org/wiki/Lie_algebra http://www.jmilne.org/math/index.html
From playlist Algebra
Gregory Arone: Calculus of functors and homotopy theory (Lecture 2)
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Seminar on Functor Calculus and Chromatic Methods" Abstract: The derivatives of a functor have a bimodule structure over a certain operad. If the Tate homology of the derivatives vanish, then
From playlist HIM Lectures: Junior Trimester Program "Topology"
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
Benoit Fresse: Rational homotopy theory, the little discs operads and graph complexes (Lecture 2)
The little cubes operads (and the equivalent little discs operads) were introduced by Boardman-Vogt and May for the study of iterated loop spaces. The study of the little cubes operads has been completely renewed during the last decade and new applications of these objects have been discov
From playlist HIM Lectures: Junior Trimester Program "Topology"
Benoit Fresse: Rational homotopy theory, the little discs operads and graph complexes (Lecture 3)
The little cubes operads (and the equivalent little discs operads) were introduced by Boardman-Vogt and May for the study of iterated loop spaces. The study of the little cubes operads has been completely renewed during the last decade and new applications of these objects have been discov
From playlist HIM Lectures: Junior Trimester Program "Topology"
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
Little disks operads and Feynman diagrams – Thomas Willwacher – ICM2018
Mathematical Physics | Topology Invited Lecture 11.3 | 6.5 Little disks operads and Feynman diagrams Thomas Willwacher Abstract: The little disks operads are classical objects in algebraic topology which have seen a wide range of applications in the past. For example they appear prominen
From playlist Mathematical Physics
David Spivak - Sense-making: accounting for intelligibility - IPAM at UCLA
Recorded 19 February 2022. David Spivak of the Topos Institute presents "Sense-making: accounting for intelligibility" at IPAM's Mathematics of Collective Intelligence Workshop. Abstract: A mathematical field can be thought of as an accounting system: we use arithmetic in finance to accoun
From playlist Workshop: Mathematics of Collective Intelligence - Feb. 15 - 19, 2022.
Tashi Walde: 2-Segal spaces as invertible infinity-operads
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: We sketch the theory of (infinity-)operads via Segal dendroidal objects (due to Cisinski, Moerdijk and Weiss). We explain its relationship with the theory
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Associahedra: The Shapes of Multiplication | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi What happens when you multiply shapes? This is part 2 of our episode on multiplying things that aren't numbers. You can check out part 1: The Multiplication Multiverse
From playlist An Infinite Playlist
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
Feynman categories, universal operations and master equations - Ralph Kaufmann
Ralph Kaufmann Purdue University; Member, School of Mathematics December 6, 2013 Feynman categories are a new universal categorical framework for generalizing operads, modular operads and twisted modular operads. The latter two appear prominently in Gromov-Witten theory and in string field
From playlist Mathematics
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
Johan Alm: Brown's dihedral moduli space and freedom of the gravity operad
Abstract: Ezra Getzler's gravity cooperad is formed by the degree-shifted cohomology groups of the open moduli spaces M_{0,n}. Francis Brown introduced partial compactifications of these moduli spaces, denoted M_{0,n}^δ. We prove that the (nonsymmetric) gravity cooperad is cofreely cogener
From playlist HIM Lectures: Junior Trimester Program "Topology"
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
Bertrand Toën - Deformation quantization and derived algebraic geometry
Bertrand TOËN (CNRS - Univ. de Montpellier 2, France)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur