---
title: Lie Group Representations
description: This topic covers how continuous symmetry groups act linearly on vector spaces. Learners will understand how to decompose representations into irreducible components, analyze character theory, and apply these mathematical structures to quantum mechanics and particle physics.
category: mathematics
subcategory: representation-theory
difficulty: beginner, intermediate, advanced
url: /subject/lie-group-representations
---

# Lie Group Representations

This topic covers how continuous symmetry groups act linearly on vector spaces. Learners will understand how to decompose representations into irreducible components, analyze character theory, and apply these mathematical structures to quantum mechanics and particle physics.

## Available Resources

1 Courses • 2 Websites

## Courses

### 1. Lie Groups and Lie Algebras

Learn Lie groups and Lie algebras with this course by Richard Borcherds! Explore lie-group-representations and build a strong foundation.

**Difficulty:** Advanced | **Price:** Free

**Link:** https://www.youtube.com/playlist?list=PLN_4R2IuNuuRgJb00X2J53Iq9qe7k1nyr

**Tags:** lie-groups, lie-algebras, representation-theory, root-systems

## Websites

### 1. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

### 2. nLab

Collaborative wiki for mathematics, physics and philosophy written from a category-theoretic viewpoint, with cross-linked entries on categories, functors, adjunctions, topos theory, higher category theory and homotopy theory. Readers can look up precise definitions, examples and references for advanced structural mathematics.

**Difficulty:** Advanced | **Language:** English | **Price:** Free

**Link:** https://ncatlab.org

**Tags:** category-theory, higher-category-theory, topos-theory, homotopy-theory, reference-wiki

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