Ternary Codes and Vertex Operator Algebras

ℤ3symmetry and W3algebra in lattice vertex operator algebras

“…We also recall certain properties of the vertex operator algebra V √ 2A 2 (cf. [23]). Let α 1 , α 2 be the simple roots of type A 2 and set α 0 = −(α 1 + α 2 ).…”

“…are the sets of all inequivalent irreducible modules for M 0 k and M 0 t , respectively ([21], [23] and [24]). We also have…”

“…The subalgebra M 0 t -modules and their fusion rules are determined in [23] and [28]. The Virasoro element…”

“…which is denoted by q in [23]. The vector v t is a highest weight vector in M 0 t of highest weight 3 for Vir(ω 3 ).…”

“…The subalgebra Vir(ω i ) generated by ω i is the Virasoro vertex operator algebra L(c, 0), which is the irreducible unitary highest weight module for the Virasoro algebra with central charge c and highest weight 0. The structure of V L as a module for Vir(ω 1 ) ⊗ Vir(ω 2 ) ⊗ Vir(ω 3 ) was discussed in [23]. Among other things it was shown that V L contains a subalgebra of the form L(4/5, 0) ⊕ L(4/5, 3).…”