What is...modular representation theory?

Here is a nice funfact explaining the connection between the cardinality of G and the trivial idempotent (which I learned through some talk). If you are looking at modules over a (f.d.) hopf algebra the following are equivalent: -The category is semisimple, -the trivial module is projective, -there exists at least one projective module whose dimension is non zero viewed as element in the ground field.

Off topic question: Are you doing olympiad maths in your freetime ?

Very good.
What is the computer program, you are using?