Classification of real Lie superalgebras based on a simple Lie algebra, giving rise to interesting examples involving ${\mathfrak {su}}(2,2)$su(2,2)

Abstract

Finite dimensional semisimple real Lie superalgebras are described via finite dimensional semisimple complex Lie superalgebras. As an application of these results, finite dimensional real Lie superalgebras $\mathfrak {m}=\mathfrak {m}_0 \oplus \mathfrak {m}_1$m=m0⊕m1 for which $\mathfrak {m}_0$m0 is a simple Lie algebra are classified up to isomorphism.