... sequence.Annals of Mathematics Automorphism groups of finite dimensional simple algebras By Nikolai L. Gordeev and Vladimir L. Popov* FINITE DIMENSIONAL SIMPLE ALGEBRAS 1059Proposition ... that many (Galois)cohomological invariants of algebraic groups are defined via realizations of groups as the automorphism groups of some finite dimensional algebras, cf. [Se],[KMRT], [SV]. These ... the k-group k-iso-morphic to SL(U)S. FINITE DIMENSIONAL SIMPLE ALGEBRAS 1053Proof. As Aut(D(L, U, S, γ, δ, Φ)) is the image of the k-homomorphism of k -groups SL(U)S→ GL(vect(D(L, U, S, γ,...