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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 …

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 …

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 …

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 …

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 …

The Wikipedia article Odd order theorem is worth reading.

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?

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 …

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 …