Orthogonal abelian Cartan subalgebra decomposition of 𝔰𝖑_n over a finite commutative ring

ABSTRACT

Orthogonal decomposition of the special linear Lie algebra over the complex numbers was studied in the early 1980s and attracted further attentions in the past decade due to its application in quantum information theory. In this paper, we study this decomposition problem of the special linear Lie algebra over a finite commutative ring with identity.

KEYWORDS:

• Abeian Cartan subalgebras
• killing form
• local ring
• orthogonal decomposition

AMS SUBJECT CLASSIFICATIONS:

• Primary: 17B50
• Secondary: 13M05

Acknowledgements

The authors would like to thank the referee for the constructive comments that lead to the improvement of this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Simons Foundation [grant number 416937].