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We study l-independence of monodromy groups G_l of any compatible system ofl-adic representations (in the sense of Serre) of number field K assumingsemisimplicity. We prove that the formal character of the derived group of theidentity component of G_l is independent of l and the (complexified) Liealgebra g_l of G_l satisfies an equal-rank subalgebra equivalence for all l.This equivalence is equivalent to the l-independence of the number of A_nfactors for all n belonging to {6,9,10,11,...} and the parity of A_4 factors ing_l.

Monodromy of Galois representations and equal-rank subalgebra equivalence