Semisimple Lie algebra

Semirings that are finite and have infinity

Semirings. You can find the simple python script here: https://gist.github.com/Nikolaj-K/f036fd07991fce26274b5b6f15a6c032 Previous video: https://youtu.be/ws6vCT7ExTY

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

Lie groups: Lie algebras

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

15 Properties of partially ordered sets

When a relation induces a partial ordering of a set, that set has certain properties with respect to the reflexive, (anti)-symmetric, and transitive properties.

From playlist Abstract algebra

Jean Michel : Quasisemisimple classes

Abstract: This is a report on joint work with François Digne. Quasisemisimple elements are a generalisation of semisimple elements to disconnected reductive groups (or equivalently, to algebraic automorphisms of reductive groups). In the setting of reductive groups over an algebraically c

From playlist Lie Theory and Generalizations

Axioms of Lie algebra theory

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

GT14. Semidirect Products

EDIT: At 6:24, the product should be "(e sub H, e sub N)", not "(e sub H, e sub G)" Abstract Algebra: Using automorphisms, we define the semidirect product of two groups. We prove the group property and construct various examples, including the dihedral groups. As an application, we

From playlist Abstract Algebra

Representations of finite groups of Lie type (Lecture - 3) by Dipendra Prasad

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

Anton Alekseev: Poisson-Lie duality and Langlands duality via Bohr-Sommerfeld

Abstract: Let G be a connected semisimple Lie group with Lie algebra 𝔤. There are two natural duality constructions that assign to it the Langlands dual group G^∨ (associated to the dual root system) and the Poisson-Lie dual group G^∗. Cartan subalgebras of 𝔤^∨ and 𝔤^∗ are isomorphic to ea

From playlist Topology

David Zywina, Computing Sato-Tate and monodromy groups.

VaNTAGe seminar on May 5, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.

From playlist The Sato-Tate conjecture for abelian varieties

AlgTopReview4: Free abelian groups and non-commutative groups

Free abelian groups play an important role in algebraic topology. These are groups modelled on the additive group of integers Z, and their theory is analogous to the theory of vector spaces. We state the Fundamental Theorem of Finitely Generated Commutative Groups, which says that any such

From playlist Algebraic Topology

Representation of finite groups over arbitrary fields by Ravindra S. Kulkarni

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

Representation theory and geometry – Geordie Williamson – ICM2018

Plenary Lecture 17 Representation theory and geometry Geordie Williamson Abstract: One of the most fundamental questions in representation theory asks for a description of the simple representations. I will give an introduction to this problem with an emphasis on the representation theor

From playlist Plenary Lectures

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

Semisimple $\mathbb{Q}$-algebras in algebraic combinatorics by Allen Herman

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

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

Paolo Piazza: Proper actions of Lie groups and numeric invariants of Dirac operators

HYBRID EVENT shall explain how to define and investigate primary and secondary invariants of G-invariant Dirac operators on a cocompact G-proper manifold, with G a connected real reductive Lie group. This involves cyclic cohomology and Ktheory. After treating the case of cyclic cocycles a

From playlist Lie Theory and Generalizations

Group automorphisms in abstract algebra

Group automorphisms are bijective mappings of a group onto itself. In this tutorial I define group automorphisms and introduce the fact that a set of such automorphisms can exist. This set is proven to be a subgroup of the symmetric group. You can learn more about Mathematica on my Udem

From playlist Abstract algebra

Oded Yacobi: Cylindrical KLR algebras and slices in the affine Grassmannian

The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: I will give an overview of a program to study quantizations of slices in the affine Grassmannian of a semisimple group G. The slices are interesting Poiss

From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"