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
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 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
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 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: 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
Markus Pflaum: The transverse index theorem for proper cocompact actions of Lie groupoids
The talk is based on joint work with H. Posthuma and X. Tang. We consider a proper cocompact action of a Lie groupoid and define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
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
Jonathan Block: Singular foliations and characteristic classes
Talk by Jonathan Rosenberg in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on October 21, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Rafael Díaz: Deformations of N-differential graded algebras
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebra
Julien Grivaux - The Lie algebra attached to a tame closed embedding
Abstract: If X is a smooth closed subscheme of an ambient smooth scheme Y, Calaque, Caldararu and Tu have endowed the shifted normal bundle NX/Y[−1] with a derived Lie algebroid structure. This structure generalizes the Lie algebra structure on the shifted tangent bundle TX[−1] on a smoot
From playlist Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday
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
Henrique Bursztyn: Relating Morita equivalence in algebra and geometry via deformation quantization
Talk by Henrique Bursztyn in Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/3225/ on April 2, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Ryszard Nest: Formality for algebroid stacks
The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. (19.09.2014) This video was created and edited with kind support from eCampus Bonn and is also available at https://mediaserver.uni-bonn.de.
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Cohomology of algebroids and harmonic shuffle relation - Tomohide Terasoma
Geometry and Arithmetic: 61st Birthday of Pierre Deligne Tomohide Terasoma University of Tokyo October 18, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a four-day c
From playlist Pierre Deligne 61st Birthday
Konstantin Ardako - Equivariant D- modules on rigid analytic spaces
Séminaire Paris Pékin Tokyo / Mercredi 17 décembre 2014 Abstract : Given a curve over a dvr of mixed characteristic 0-p with smooth generic fiber and with semistable reduction, I will present a criterion for good reduction in terms of the (unipotent) p-adic étale fundamental group of its
From playlist Conférences Paris Pékin Tokyo
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
Geometry Of The Hitchin Integrable Systems, And Some Variations (Lecture 2) by Jacques Hurtubise
PROGRAM : QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS : Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)