On simple symplectic alternating algebras and their groups of automorphisms

Let N be any perfect symplectic alternating algebra. We show that N can be embedded into a larger simple alternating algebra S of dimension 7⋅(dimN)+6 such that Aut (S)={id}. This answers a question raised in [9]. Building on this result we show moreover that for any finite group G and characteristic c there exists a symplectic alternating algebra L over a field F of characteristic c such that Aut (L)=G.