Certain extensions of vertex operator algebras of affine type

Abstract

We generalize Feigin and Miwa's construction of extended vertex operator (super)algebras $A_k(sl(2))$ for other types of simple Lie algebras. For all the constructed extended vertex operator (super)algebras, irreducible modules are classified, complete reducibility of every module is proved and fusion rules are determined modulo the fusion rules for vertex operator algebras of affine type.

Latex, 51 pages

References in corpus (5)

• Simple currents and extensions of vertex operator algebras
• Annihilating fields of standard modules of sl(2,C)~ and combinatorial identities
• Representation theory and tensor product theory for vertex operator algebras
• The action of outer automorphisms on bundles of chiral blocks
• Extended vertex operator algebras and monomial bases

Cited by in corpus (9)

• Supersymmetry and the Suzuki chain
• Automorphism groups and uniqueness of holomorphic vertex operator algebras of central charge $24$
• Quantum dimensions and irreducible modules of some diagonal coset vertex operator algebras
• On abelian generalized vertex algebras
• Trace functions and fusion rules of diagonal coset vertex operator algebras
• Level-Rank Duality for Vertex Operator Algebras of types B and D
• Loop groups and noncommutative geometry
• Automorphism groups of the holomorphic vertex operator algebras associated with Niemeier lattices and the $-1$-isometries
• On a symmetry of the category of integrable modules