Lie algebra Articles

Tag Archive for: Lie algebra

lie group physics

When Lie Groups Became Physics

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Abstract We explain by simple examples (one-parameter Lie groups), partly in the original language, and along the historical papers of Sophus Lie, Abraham…
Lie Algebra Intro

Lie Algebras Explained: Commutators, SU(2), SO(3), Euc(n)

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A Lie algebra is the vector space of infinitesimal generators attached to a Lie group at its identity element, equipped with a bilinear antisymmetric commutator…
lie algebra representations

Learn Lie Algebras: A Walkthrough – The Representations

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  Part III: Representations  Sums and Products. Frobenius began in ##1896## to generalize Weber's group characters and soon investigated…
Lie Algebra Structure

Learn Lie Algebras: A Walkthrough – The Structures

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  Part II: StructuresDecompositions.Lie algebra theory is to a large extend the classification of the semisimple Lie algebras which…
lie algebra basics

Learn Lie Algebras: A Walkthrough – The Basics

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  Part I: Basics Introduction. This article is meant to provide a quick reference guide to Lie algebras: the terminology, important theorems,…
manifold2

A Journey to The Manifold SU(2): Representations

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Part 1 Image source: [23]  Some useful bases of ##\mathfrak{su}(2,\mathbb{C})## Notations can differ from author to author: the…
deriitive4

The Pantheon of Derivatives – Lie Derivatives And Others (IV)

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  Lie Derivatives A Lie derivative is in general the differentiation of a tensor field along a vector field. This allows several applications…
relativitygauge

Exploring General Relativity as a Gauge Theory

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The fundamental interactions of the Standard Model are described by Yang-Mills theory. This is a gauge theory, which means the following: (1) Choose a…
supergravity

Emergence From the Superpoint

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 In the previous article we saw that the generalization of super-Lie algebras to homotopy super-Lie n-algebras (super L-infinity algebras)…