Two parameter deformation of Grassmann matrix group and supergroup Available to Purchase

The two parameter quantum deformations of 2×2 Grassmann matrices, Gr(2), and supermatrices, Gr(1|1), are presented. Gr(2) whose matrix elements are all Grassmannian variables is called the superdual of the general linear group GL(2), and Gr(1|1) whose diagonal matrix elements are Grassmannian variables is called the superdual of the supergroup GL(1|1) whose nondiagonal elements are Grassmannian. Noncentral dual superdeterminant for Grassmann supermatrices belonging to Gr_p,q(1|1) is constructed. As with the 2×2 quantum matrices, the relations satisfied by the matrix elements of the Grassmann matrices and supermatrices are expressed in terms of an R̂ matrix. The properties of the nth power of a Grassmann supermatrix are given as an Appendix.