As I understand it, the symplectic Lie group Sp(2n,R) of 2n×2n symplectic matrices is generated by the matrices in http://en.wikipedia.org/wiki/Symplectic_group#Infinitesimal_generators . Does this mean that sl(n,R) is a subalgebra of the corresponding lie algebra, since in that formula we can truncate by removing the matrices B and C and enforce that A is traceless? Also, sp(4,R) has dimension 10 and sl(3,R) has dimension 8. Is sl(3,R) a subalgebra of sp(4,R) or not? As a more practical question, where should I look if I want to look up these kind of standard results on standard Lie groups? Googling did not take me very far.