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Your argument fails because the bracket can (sometimes) take pairs of elements into the centre. Therefore the direct sum as vector spaces isn't necessarily a direct sum of Lie algebras. For nilpotent …

See http://en.wikipedia.org/wiki/Unitary_representation for the representation theory. You can follow the links from http://en.wikipedia.org/wiki/Simple_Lie_group#Exceptional_cases to find external li …

The Wikipedia article Odd order theorem is worth reading.

Isn't this just a fancy way of talking about the cycle decomposition of a permutation? The language you use is a little imprecise. But, firstly, by change of basis P can be made into a block matrix fo …

You should really study the representation theory in the wider context of a semidirect product. George Mackey wrote the basic theory on this, and you'll almost certainly understand more by working out …

You have a (real) linear representation r of the cyclic group C of order d; you give its character, and then ask for the character of a certain subrepresentation of the tensor product of r and its dua …

For a mathematician $k$ would be more logical (reflection symmetry in the alphabet)? But confusing because $k$ is a field ... so take one step more. Any better explanations?

The conventional real Clifford algebras are matrix algebras over the real numbers, complex numbera, or quaternions, and are simple algebras in the sense of ring theory. Any subalgebra that is a simple …

I don't know why you say the Dedekind problem is "forgotten": the Dedekind determinant is discussed in number theory books. The factorisation for the regular representation for general finite groups w …