dimpas - a subalgebra of su(2^n)

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.
, ,
Should be well-known to people doing quantum algorithms, etc.