Verlinde algebra

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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 rational two-dimensional conformal field theory, whose structure constants Nν
describe fusion of primary fields.

Verlinde formula[edit]

In terms of the modular S-matrix, the fusion coefficients are given by[1]

where is the component-wise complex conjugate of .

Twisted equivariant K-theory[edit]

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. For this special case Freed, Hopkins & Teleman (2001) showed that the Verlinde algebra can be identified with twisted equivariant K-theory of G.

See also[edit]


  1. ^ Blumenhagen, Ralph (2009). Introduction to Conformal Field Theory. Plauschinn, Erik. Dordrecht: Springer. pp. 143. ISBN 9783642004490. OCLC 437345787.