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

TL;DR

This paper introduces the Quotient Algebra Partition (QAP), a universal algebraic structure for Lie algebras, facilitating systematic Cartan decompositions, demonstrated through the su(N) algebra using spinor representation.

Contribution

It presents the QAP framework for Lie algebras and applies it to su(N), enabling algorithmic Cartan decompositions with a focus on spinor representations.

Findings

QAP is a universal structure for Lie algebras

Enables algorithmic Cartan decompositions

Applied to su(N) using spinor representation

Abstract

An algebraic structure, Quotient Algebra Partition or QAP, is introduced in a serial of articles. The structure QAP is universal to Lie Algebras and enables algorithmic and exhaustive Cartan decompositions. The first episode draws the simplest form of the structure in terms of the spinor representation.