Algebras with Involution and Classical Groups

Abstract

Deep relations between linear algebraic groups over an arbitrary field and central simple algebras with involution can be traced back to two main sources. In [40], Weil1 shows that the connected component of the identity in the automorphism group of a separable algebra with involution is almost2 always a semisimple linear algebraic group of adjoint type and that, conversely, almost3 every semisimple linear algebraic group of adjoint type can be obtained in this way. The groups derived from algebras with involution are called classical.