The representation of groups by automorphisms of forms

Abstract

In the present paper the formal apparatus of the preceding one1 (cf. [4], always to be quoted as I) will be applied to study representations of groups, and specifically of finite groups by automorphisms of forms over a commutative ring R with involution, which may bc the trivial one. When R is a field of characteristic other than 2 then our theory covers orthogonal and symplectic representations (for trivial involution) and unitary representations (for nontrivial involution). From the traditional point of view one would start with a form ,B with underlying R-module M, i.e. with a map