Finite-Dimensional Lie Algebras and Their Representations for Unified Model Building

TL;DR

This paper provides a comprehensive analysis of finite-dimensional Lie algebras and their representations, focusing on their application in grand unified theories in four and five dimensions, including detailed algebraic properties and classification data.

Contribution

It offers detailed classification data and tools for applying Lie algebras to model building in higher-dimensional grand unified theories, extending previous work up to rank-20.

Findings

Classification of Lie algebras suitable for GUTs in 4 and 5 dimensions

Explicit formulas for representations and invariants

Identification of applicable Lie algebras for model building

Abstract

We give information about finite-dimensional Lie algebras and their representations for model building in 4 and 5 dimensions; e.g., conjugacy classes, types of representations, Weyl dimensional formulas, Dynkin indices, quadratic Casimir invariants, anomaly coefficients, projection matrices, and branching rules of Lie algebras and their subalgebras up to rank-20. We show what kind of Lie algebras can be applied for grand unified theories in 4 and 5 dimensions.