Gatf. Dacosta et L. Oraifeartaigh, NONTRIVIAL NONCANONICAL W-ALGEBRAS FROM KAC-MOODY REDUCTIONS, Physics letters. Section B, 333(3-4), 1994, pp. 353-363
By reducing a split G2 Kac-Moody algebra by a non-maximal set of first
-class constraints we produce W-algebras which (i) contain fields of n
egative conformal spin and (ii) are not trivial extensions of canonica
l W-algebras.