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
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 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 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
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 25 - the commutator and the Lie Algebra
Lie Groups and Lie Algebras: Lesson 25 - the commutator In this lecture we discover how to represent an infinitesimal commutator of the Lie group using a member of the Lie algebra. We promote the vector space spawned by the group generators to an algebra. Please consider supporting this
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 12 - The Classical Groups Part X (redux)
Lie Groups and Lie Algebras: Lesson 12 - The Classical Groups Part X (redux) We name the classical groups, finally! This video ended a bit short, I added the missing part in the "redux" version of this lesson. Please consider supporting this channel via Patreon: https://www.patreon.com/
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
Askold Khovanskii: Complex torus, its good compactifications and the ring of conditions
Abstract: Let X be an algebraic subvariety in (ℂ∗)n. According to the good compactifification theorem there is a complete toric variety M⊃(ℂ∗)n such that the closure of X in M does not intersect orbits in M of codimension bigger than dimℂX. All proofs of this theorem I met in literature ar
From playlist Algebraic and Complex Geometry
Francesc Fité, Sato-Tate groups of abelian varieties of dimension up to 3
VaNTAGe seminar on April 7, 2020 License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
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
Lie Groups and Lie Algebras: Lesson 30 - SL(1,Q) from sl(1,Q)
Lie Groups and Lie Algebras: Lesson 30 - SL(1,Q) from sl(1,Q)' I this lecture we examine the lesser known member of the three Lie groups that share the "angular momentum" algebra: The Special Linear Group of transformations of a one dimensional quaternionic vector space. This is an exampl
From playlist Lie Groups and Lie Algebras
The Fundamental Domain | The Geometry of SL(2,Z), Section 1.2
The fundamental domain for SL(2,Z) on the complex upper half plane is described, with proof. We also derive the stabilizers of the action, and provide generators for SL(2,Z). My Twitter: https://twitter.com/KristapsBalodi3 Description of the Fundamental Domain:(0:00) Statement of Main T
From playlist The Geometry of SL(2,Z)