Gradings on $o(8,\mathbb C)$

TL;DR

This paper provides a comprehensive classification of all fourteen fine group gradings on the complex Lie algebra o(8,C), offering a detailed matricial description.

Contribution

It presents the complete list and explicit descriptions of all fine group gradings on o(8,C), expanding understanding of its algebraic structure.

Findings

Identified all fourteen fine group gradings on o(8,C)

Provided explicit matricial descriptions for each grading

Enhanced the classification framework for complex Lie algebras

Abstract

This is a matricial description of all the fine group gradings on the exceptional Lie algebra $o(8,\mathbb C)$. There are fourteen.