Prime subfield enveloping algebra in Magma

Question

Given a matrix group G $\leq$ GL(d, K), I can create the subalgebra of Mat$_{d}$(K) consisting of all K-linear combinations of the elements of G using the MatrixAlgebra<K, d | L> constructor. I can't, however, create the subalgebra of Mat$_{d}$(K) consisting of all K$_{0}$-linear combinations of the elements of G where _K_$_{0}$ is the prime subfield of K. Is there a way of creating such an object in MAGMA?

Answer 1

I think you can do this with an alternate MatrixAlgebra usage; put

A = MatrixAlgebra(K,d | L);

then to convert it over the basefield put

B := MatrixAlgebra(A, PrimeField(K));

this will give, as a second return value, a map to convert over just specific matrices if you like.