The subalgebras of the generalized special unitary algebra $\mathfrak{su}(2,1)$

Abstract

We classify the real subalgebras of the generalized special unitary algebra $\mathfrak{su}(2,1)$, a non-compact real form of the complex special linear algebra $\mathfrak{sl}_3(\mathbb{C})$. Our approach combines Galois cohomology with the existing classification of complex subalgebras of $\mathfrak{sl}_3(\mathbb{C})$. This work completes the classification of real subalgebras of the non-compact real forms of $\mathfrak{sl}_3(\mathbb{C})$, since those of $\mathfrak{sl}_3(\mathbb{R})$ have already been classified.