Irreducible representation of dihedral group

Let D_n be the dihedral group. Classify the irreducible representations of D_n over C (complex).

SO(4) isomorphic

Show that SO(4) is isomorphic to the quotient of SU(2) X SU(2) by the subgroup generated by (-1,1)

Mathematical system

I am having a problem drawing the table for the following system: Define a universal set U as the set of counting numbers. Form a new set that contains all possible subsets of U. This new set of subsets together with the operation of set intersection forms a mathematical system. Then I have to tell which properties that we did in class are satisfied by the system, which I would not have a problem with if I could just get the table drawn.

Indecomposable representations of quivers

Classsify the indecomposable representations of the following quivers: 1. o -> o <- o 2. o -> o <- o ^ l o

Modern Algebra, Group Theory (I): G contains all symbols ai, i = 0,1,2, …….,n-1 where we insist that a0 = an = e, ai.aj = ai+j if i+j ≤ n and ai.aj = ai+j-n if i+j > n .To prove that G is a cyclic group of order n.

Modern Algebra Group Theory (I) G contains all symbols a^i, i = 0,1,2, …….,n-1 where we insist that a^0 = a^n = e, a^i.a^j = a^(i+j) if i+j ≤ n and a^i.a^j = a^(i+j-n) if i+j > n . To prove that G is a cyclic group of order n.