Math/Physic/Economic/Statistic Problems
01 0). Let = E M2(C) = —sxL where s = Argue that 6 is a real vector space and find a basis for IL
(ii) Show that 4 is a Lie algebra if we set = xy — yx for all x, y E h.Determine whether 6 is simple.
et {e, h, f} and {x, y,z} be bases for Ai with Lie products [h, e] = 2e, [h, = —2f, [e, = h
and
[x, y] = 2x + 2y, [y, z] = 2y + 2z, k, x]= 2z + 2x. Find functions gam, gy and gr such that x 1—> g(e,h), y ,g„(h), z H gr(h, f), defines an automorphism ofAi.