Constructions for \(A\)-Modules#
- RModule(A): AlgMat -> ModRng#
Given a subalgebra \(A\) of \(M_n(K)\), create the right \(A\)-module \(M\) with underlying vector space \(K^{(n)}\), where the action of \(a \in A\) is given by \(m*a\), \(m \in M\).
- RModule(Q): [ MtrxS ] -> ModTupRng#
Given the subalgebra \(A\) of \(M_n(K)\) generated by the terms of the sequence \(Q\), create the right \(A\)-module \(M\) with underlying vector space \(K^{(n)}\), where the action of \(a \in A\) is given by \(m*a\), \(m \in M\).
- Example: Create K6 (ex-2aced1)#
We construct the \(6\)-dimensional module over \({\bf F}_{2}\) with an action given by the matrices
\[\begin{split}\begin{pmatrix}1&0&0&1&0&1\\ 0&1&0&0&1&1\\ 0&1&1&1&1&0\\ 0&0&0&1&1&0\\ 0&0&0&1&0&1\\ 0&1&0&1&0&0\end{pmatrix}\qquad\qquad \begin{pmatrix}0&1&1&0&1&0\\ 0&0&1&1&1&1\\ 1&0&0&1&0&1\\ 0&0&0&1&0&0\\ 0&0&0&0&1&0\\ 0&0&0&0&0&1\end{pmatrix}\end{split}\]> A := MatrixAlgebra<GF(2), 6 | > [ 1,0,0,1,0,1, > 0,1,0,0,1,1, > 0,1,1,1,1,0, > 0,0,0,1,1,0, > 0,0,0,1,0,1, > 0,1,0,1,0,0 ], > [ 0,1,1,0,1,0, > 0,0,1,1,1,1, > 1,0,0,1,0,1, > 0,0,0,1,0,0, > 0,0,0,0,1,0, > 0,0,0,0,0,1 ] >; > M := RModule(A); > M; RModule M of dimension 6 over GF(2)