Gradings on the real form $\mathfrak{e}_{6,-14}$

TL;DR

This paper classifies six specific fine gradings on the real form _{6,-14}, derived from gradings on its complexified algebra, detailing their universal grading groups.

Contribution

It provides a complete description of six fine gradings on _{6,-14} and identifies their universal grading groups, expanding understanding of the algebra's structure.

Findings

Six fine gradings are described.

Universal grading groups are explicitly determined.

Gradings originate from complexified algebra gradings.

Abstract

Six fine gradings on the real form $\mathfrak{e}_{6,-14}$ are described, precisely those ones coming from fine gradings on the complexified algebra. The universal grading groups are $\mathbb Z_2^3\times\mathbb Z_3^2$, $\mathbb Z_2^6$, $\mathbb Z\times\mathbb Z_2^4$, $\mathbb Z_2^7$, $\mathbb Z\times\mathbb Z_2^5$ and $\mathbb Z^2\times\mathbb Z_2^3$.