In mathematics, a Verlinde algebra is a finite-dimensional associative algebra introduced by Erik Verlinde (), with a basis of elements φλ corresponding to primary fields of a two-dimensional rational conformal field theory, whose structure constants Nνλμ describe fusion of primary fields. For example, if G is a compact Lie group, there is a rational conformal field theory whose primary fields correspond to the representations λ of some fixed level of loop group of G. In this case showed that the Verlinde algebra can be identified with twisted equivariant K-theory of G.