In mathematics, a Verlinde algebra is a finite-dimensional associative algebra introduced by Erik Verlinde (1988), with a basis of elements φλ corresponding to primary fields of a two-dimensional rational conformal field theory, whose structure constants Nν
λμ 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 Freed (2001) showed that the Verlinde algebra can be identified with twisted equivariant K-theory of G.
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