Let Wk(sl4β,fsubregβ) be the universal
W-algebra associated to sl4β with its subregular
nilpotent element, and let Wkβ(sl4β,fsubregβ) be its simple quotient. There is a Heisenberg subalgebra
H, and we denote by Ck the coset
Com(H,Wk(sl4β,fsubregβ)),
and by Ckβ its simple quotient. We show that for k=β4+(m+4)/3
where m is an integer greater than 2 and m+1 is coprime to 3,
Ckβ is isomorphic to a rational, regular W-algebra
W(slmβ,fregβ). In particular,
Wkβ(sl4β,fsubregβ) is a simple current
extension of the tensor product of W(slmβ,fregβ) with a rank one lattice vertex operator algebra, and hence is
rational.Comment: 14 pages, to appear in conference proceedings for AMS Special Session
on Vertex Algebras and Geometr