Orthogonal abelian Cartan subalgebra decomposition of mathfrak{sl}_n over a finite commutative ring

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.