The Classical Groups
DOI link for The Classical Groups
The Classical Groups book
The are four infinite series of simple Lie algebras, generating what are called the classical groups. The first of these consists of the SU (N) algebras that we have studied already. Their Dynkin diagrams have the form https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429499210/01253d69-3ddc-48b4-9424-d2337a20fada/content/eq0112.tif"/> The rank n algebra SU(n + 1) was called An by Cartan, who first classified these things. In this brief section, we will go over the others very lightly, before we do the complete classification. Later, we will discuss each of them in detail.