Extended current algebras and the coset construction of conformal field theories

Abstract

We investigate extended algebras associated with coset construction. We associate a Verlinde type algebra A with the branching functions. Each allowed choice of a subalgebra B corresponds to an extended algebra whose classes of currents are in one to one correspondence with the elements of B. The subalgebra B encodes the fusion rules of the currents. The elements of A/B are in one to one correspondence with the primary fields. Each coset element corresponds to one primary field and its descendants. The fusion rules of the operator algebra are encoded in A.