On the real forms of the exceptional Lie algebra $ \mathfrak{e}_6$ and their Satake diagrams

Abstract

Satake diagrams of the real forms $ \mathfrak{e}_{6,-26}$, $ \mathfrak{e}_{6,-14}$ and $ \mathfrak{e}_{6,2}$ are carefully developed. The first real form is constructed with an Albert algebra and the other ones by using the two paraoctonion algebras and certain symmetric construction of the magic square.