Lie Group

Lie Group & Representation

Lie group and their representation are widely used math and physics.

This is such a huge topic, and this page is content list of that.



Introduction

Finite group Representation

Lie group

SU(2)

Tensor Operator

Weight and Roots

Tensor Representation

Weyl group and Character Formula

Classical Groups

Spinor Representation


Non-Compact (spacetime) Group

Euclidean Group

Lorentz Group

Poincare Group

Conformal Group


Super Lie Algebra

Supersymmetry

Batalin-Vilkovsky algebra

Gerstenhaber algebra


Geometry

Lie group is group manifold, so it can be analyzed through analysis.

In physics, Lie group act fibre bundle on spacetime manifold like gauge group.

Manifold, Differential Geometry, Fibre Bundle


Quantum Group

Poisson Lie Algebra

Introductino to quantum group

Universal Enveloping Algebra

Affine Lie Algebra

Hopf Algebra


Reference

Howard Georgi - Lie Algebras in Particle Physics

Zee - Group Theorey in a Nutshell for Physicists

Wess&Bagger - Supersymmetry and Supergravity


mf23.web.rice.edu

Quantum Groups in Two-dimensional Physics

A Guide to Quantum Group

Mathematical Quantization

Geomertrix Quantization

Quantum Theory for Mathematicians

Affine Lie Algebras and Quantum Groups


Fulton, Harris - Representation Theory A first course

Hall - Lie Groups, Lie Algebras, and Representations

Bump - Lie Groups


Kassel - Quantum Groups

Brown - Cohomology of Groups


Derksen, Kemper - Computational Invariant Theory