a subalgebra of su(2^n)

[dimpas]

What can be said about the subalgebra of the Lie algebra su(2n) generated by 3n matrices of the form E⊗...⊗E⊗A⊗E⊗...⊗E (n-fold tensor product), where E is the 2x2 identity matrix and -iA is one of the Pauli matrices, i.e.

Comments

[justpasha]

Your Lie algebra is very unhuman. Calculate in GAP?

[dimpas]

isn't it just the direct sum of n copies of su2 ?