Formal Definition
Given a group G and a field F, the elements of its representation ring RF(G) are the formal differences of isomorphism classes of finite dimensional linear F-representations of G. For the ring structure, addition is given by the direct sum of representations, and multiplication by their tensor product over F. When F is omitted from the notation, as in R(G), then F is implicitly taken to be the field of complex numbers.
Read more about this topic: Representation Ring
Famous quotes containing the words formal and/or definition:
“The formal Washington dinner party has all the spontaneity of a Japanese imperial funeral.”
—Simon Hoggart (b. 1946)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)