Quotient Algebra Partition and Cartan Decomposition for su(N) II

TL;DR

This paper advances the mathematical framework for su(N) Lie algebras by classifying Cartan subalgebras and establishing quotient algebra partitions using s-representation and subalgebra extension methods.

Contribution

It introduces a new approach to quotient algebra partitioning in su(N) using s-representation and classifies all Cartan subalgebras through recursive extension.

Findings

Classified all Cartan subalgebras of su(N).

Established quotient algebra partition under minimal conditions.

Provided a recursive method for generating Cartan subalgebras.

Abstract

This is the sequel exposition following [1]. The framework quotient algebra partition is rephrased in the language of the s-representation. Thanks to this language, a quotient algebra partition of the simplest form is established under a minimum number of conditions governed by a bi-subalgebra of rank zero, i.e., a Cartan subalgebra. Within the framework, all Cartan subalgebras of su(N) are classified and generated recursively through the process of the subalgebra extension.