  Renault, Wassermann, Handelman and Rossmann (early 1980s) and Evans and Gould
(1994) explicitly described the $K$-theory of certain unital AF-algebras $A$ as
(quotients of) polynomial rings. In this paper, we show that in each case the
multiplication in the polynomial ring (quotient) is induced by a
$*$-homomorphism $A\otimes A\to A$ arising from a unitary braiding on a
C*-tensor category and essentially defined by Erlijman and Wenzl (2007). We
also present some new explicit calculations based on the work of Gepner, Fuchs
and others. Specifically, we perform computations for the rank two compact Lie
groups SU(3), Sp(4) and G$_2$ that are analogous to the Evans-Gould computation
for the rank one compact Lie group SU(2).
  The Verlinde rings are the fusion rings of Wess-Zumino-Witten models in
conformal field theory or, equivalently, of certain related C*-tensor
categories. Freed, Hopkins and Teleman (early 2000s) realized these rings via
twisted equivariant $K$-theory. Inspired by this, our long-term goal is to
realize these rings in a simpler $K$-theoretical manner, avoiding the
technicalities of loop group analysis. As a step in this direction, we note
that the Verlinde rings can be recovered as above in certain special cases.
