1. The problem statement, all variables and given/known data Exercises: https://mega.co.nz/#!YdIgjA7T!WmgIpFjCoO-elDyPtUkDNarm21sZ_xet6OTJndPGiRY Text: https://mega.co.nz/#!pVRxVKIC!RfFZiW2atRNj9ycGa4Xx_7Nu5FO4a1e6wmyQVLCcGlQ 2. Relevant equations 3. The attempt at a solution This is what I made, obviously all help would be appreciated :): 1) Given $$( \Re, +) $$ and $$( \Re, +)$$ a defined aplication $$\phi: \Re -> \Re \Longrightarrow \phi(g+g) = \phi(g) + \phi(g) = 2\phi(g); \forall g ( \Re, +). $$ Don't know how to end this... 2) $$ O(p, N-p)$$ Don't know what is the dimension. $$SL(N,C)$$ " " ". $$SU(N)$$ has dimendion $$N²-1 -> dim = 8.$$ $$U(N)$$ has dimension $$N² -> dim = 1.$$ 3) Don't know how to work it out. 4) The transposition space. Order 3. Generator is identity. I think this is totally wrong and also do not know how to end the exercise. 5) I do not know. 6) I am almost sure how to solve it but is kinda pain in the arse to post it here. 7) No idea. No idea how to solve the last 2 exercises.