On Kac’s Jordan superalgebra

AbstractThe group-scheme of automorphisms of the 10-dimensional exceptional Kac’s Jordan superalgebra is shown to be isomorphic to the semi-direct product of the direct product of two copies of SL2 by the constant group-scheme C2 . This is used to revisit, extend and simplify, known results on the classification of the twisted forms of this superalgebra and of its gradings.