Monodromy of Galois representations and equal-rank subalgebra equivalence

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We study l-independence of monodromy groups Gₗ of any compatible system of l-adic representations (in the sense of Serre) of number field K assuming semisimplicity. We prove that the formal character of the derived group of the identity component of Gₗ is independent of l and the (complexified) Lie algebra gₗ of Gₗ satisfies an equal-rank subalgebra equivalence for all l. This equivalence is equivalent to the l-independence of the number of Aₙ factors for all n belonging to 6,9,10,11,... and the parity of A₄ factors in gₗ.