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 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
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
Lie Groups and Lie Algebras: Lesson 26: Review!
Lie Groups and Lie Algebras: Lesson 26: Review! It never hurts to recap! https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
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 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 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
Structures in the Floer theory of Symplectic Lie Groupoids - James Pascaleff
Symplectic Dynamics/Geometry Seminar Topic: Structures in the Floer theory of Symplectic Lie Groupoids Speaker: James Pascaleff Affiliation: University of Illinois, Urbana-Champaign Date: October 15, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
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"
Jean Renault: Groupoid correspondences and C*-correspondences
I will present a recent definition of correspondence for locally compact groupoids with Haar systems due to R. D. Holkar and based on previous work by M. Buneci and P. Stachura, which makes the groupoid C*-algebra construction a functor from the category of groupoids to the category of C*-
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Tristan Bice, Dauns-Hofmann-Kumjian-Renault Duality for Fell Bundles and Structured C*-Algebras
Noncommutative Geometry Seminar(Asia-Pacific), Sep. 27, 2021
From playlist Global Noncommutative Geometry Seminar (Asia and Pacific)
Erik van Erp: Pseudodifferential Calculi and Groupoids
In recent work Debord and Skandalis realized pseudodifferential operators (on an arbitrary Lie groupoid G) as integrals of certain smooth kernels on the adiabatic groupoid of G. We propose an alternative definition of pseudodifferential calculi (including nonstandard calculi like the Heise
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Tristan Bice, Dauns-Hofmann-Kumjian-Renault Duality for Fell Bundles and Structured C*-Algebras
Global Noncommutative Geometry Seminar(Asia-Pacific), Sep. 27, 2021
From playlist Global Noncommutative Geometry Seminar (Asia and Pacific)
Erik van Erp: Lie groupoids in index theory 4
The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. 12.9.2014
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Denis Perrot: Cyclic cohomology and local index theory for Lie groupoids
In this talk we will consider smooth actions of Lie groupoids on manifolds. Using cyclic cohomological methods, we will establish local higher index formulas for certain pseudodifferential-type operators. The lecture was held within the framework of the Hausdorff Trimester Program Non-com
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
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
Erik van Erp: Lie groupoids in index theory 1
The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. 9.9.2014
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
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
Symmetries of hamiltonian actions of reductive groups - David Ben-Zvi
Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound II - Amnon Ta-Shma Computer Science/Discrete Mathematics Seminar II Topic: Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound II Speaker: Amnon Ta-Shma Affiliation: Tel Aviv University Date: January 3
From playlist Mathematics