Grassmann analogs of classical matrix groups

Abstract

In general, if the parameters of a real or complex algebraic matrix group are replaced by Grassmann parameters, without changing the algebraic constraints, the resulting set fails to form a group. It is shown how to remedy this defect of naive Grassmannification by generalizing the constraint relations. In particular, it is shown how to define Grassmann analogs of the orthogonal, unitary, and symplectic groups.