Lie Algebras Courses and Certifications

Institute for Advanced Study

Lie Algebras and Homotopy Theory - Jacob Lurie

Explore connections between Lie algebras and homotopy theory, covering fundamental groups, Whitehead brackets, and Quillen's theorem in this advanced mathematics seminar.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

QuantumTopology

Brunnian Braids and Lie Algebras

Explore the fascinating connection between Brunnian braids and Lie algebras in this advanced mathematical lecture by Vladimir Vershinin, delving into complex topological structures.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Fields Institute

On Conjugacy of Cartan Subalgebras in Extended Affine Lie Algebras and Classification of Torsors

Explore advanced concepts in extended affine Lie algebras and torsors over Laurent polynomial rings in this mathematical lecture by Vladimir Chernousov at the Fields Institute.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

A New Look at Lie Algebras - Geometric Construction and Invariants

Explore a novel approach to understanding real finite-dimensional Lie algebras through eigenvalue problems, focusing on solvable algebras and their relationship with Lie-Poisson structures.

• YouTube
• 40 minutes
• On-Demand
• Free Video

BIMSA

Statistics of Large Tensor Products of Representations of Simple Lie Algebras

Delve into advanced mathematical concepts exploring asymptotic behavior of multiplicities in tensor products of simple Lie algebra representations, with focus on irreducible components and Plancherel measures.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Lie Algebras of Diffeomorphism Groups of Non-compact Manifolds - Part 1

Delve into advanced mathematical concepts exploring diffeomorphism groups of non-compact manifolds, focusing on their Lie algebra structures and elastic properties in diffeological spaces.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

INI Seminar Room 2

Okounkov's Conjecture via BPS Lie Algebras

Delve into Okounkov's conjecture and its proof through BPS Lie algebras, exploring connections between Yangian algebras, quiver varieties, and Kac polynomials in algebraic geometry.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Fields Institute

Associated Lie Algebras of Right-Angled Coxeter Groups and Homotopy Theory

Explore the connection between associated Lie algebras of right-angled Coxeter groups and their applications in homotopy theory through advanced mathematical analysis.

• YouTube
• 29 minutes
• On-Demand
• Free Video

M-Seminar, Kansas State University

Maulik-Okounkov Lie Algebras and BPS Lie Algebras

Explore the connection between Maulik-Okounkov and BPS Lie algebras, examining their roles in quiver varieties and cohomological DT theory. Gain insights into non-abelian stable envelopes and Okounkov's conjecture.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

The Wronskians over Multidimension and Homotopy Lie Algebras

Explore multidimensional Wronskian determinants and their connection to homotopy Lie algebras, extending classical linear independence tests to higher dimensions and uncovering new algebraic structures.

• YouTube
• 43 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Kinematical Lie Algebras and Their Role in Physics

Explore kinematical Lie algebras and their fundamental applications in theoretical physics through expert mathematical analysis.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Mathemaniac

Lie Groups, Algebras, and Brackets - Visual Introduction to Lie Theory

Discover Lie theory through visual intuition, exploring groups, algebras, rotations in higher dimensions, exponentials, matrix operations, and the geometric meaning behind abstract concepts.

• YouTube
• 2 hours 17 minutes
• On-Demand
• Free Video

Michael Penn

The Derivative Is a Lie

Explore the concept of derivatives through a whimsical narrative, blending mathematical concepts with creative storytelling to make complex ideas more accessible and engaging.

• YouTube
• 23 minutes
• On-Demand
• Free Video

IISc Bangalore;  NPTEL

Introduction to Lie Algebras

Explore finite-dimensional Lie algebras, from basic definitions to advanced concepts like root space decomposition. Gain insights into nilpotent, solvable, and semi-simple Lie algebras.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

Centre de recherches mathématiques - CRM

Extensions of Affine Algebra Vertex Operator Algebras

Explore extensions of affine algebra VOAs, focusing on V(g,k) for simple Lie algebras. Learn about finite-index extensions, simple currents, and quantum subgroups in module category classification.

• YouTube
• 54 minutes
• On-Demand
• Free Video