Non-linear Twice Extension Of Linear Modules Over Exterior Algebras

Let V be a vector space,Λ=ΛV is a exterior algebra over V . a,b are linearindependence elements over V . t, n are positive integers, letis matrix overΛ. Such linear modules—their representation matrix is Fn1(a,b) arecalled minimal linear module of complexity two with cyclic length n.Let a,b,c be linear independence vectors over V , we discussed extensionproblem of three minimal linear modules M, L, H of representation matrices1. The elements of the former m columns of W1 are zero, the elements of thelatter n columns of W1 belong to L(ab,bc). The elements of the former m + 1columns of W2 are zero, the elements of the last column of W2 are zero, the otherselements belong to L(bc).(?) the elements of the former m columns of W1, Y₁ are zero, the elements of the lattern columns of W1, Y₁ belong to L(ab,bc). We proved the following results:...