A note on orthogonal decomposition of 𝔰𝔩n over commutative rings

Abstract

The orthogonal decomposition (OD) of special linear Lie algebras over the complex numbers was first explored in the early 1980s and has gained renewed interest in the past decade due to its applications in quantum information theory. In this study, we investigate the OD of special linear Lie algebras over commutative rings with identity. Additionally, we present examples of specific rings that facilitate the existence of such ODs for these Lie algebras.

Keywords

• cartan subalgebra
• killing form
• orthogonal decomposition
• 17b50
• 13m05