Kenichiro Tanabe

Fixed point subalgebras of lattice vertex operator algebras by an automorphism of order three

We study the fixed point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. We classify the irreducible modules for the subalgebra. Moreover, the rationality and the

Finite-dimensional modules for the polynomial ring in one variable as a vertex algebra

C_2

A generalization of twisted modules over vertex algebras

-cofiniteness of the subalgebra are established. Our result contains the case of the vertex operator algebra associated with the Leech lattice.

Finite-dimensional vertex algebra modules over fixed point differential subfields

Abstract A commutative associative algebra A over C with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for vertex algebra A and the modules for associative algebra A are not well understood. In this paper, I give the classification of finite-dimensional indecomposable untwisted or twisted modules for the polynomial ring in one variable over C as a vertex algebra.

Simple weak modules for the fixed point subalgebra of the Heisenberg vertex operator algebra of rank 1 by an automorphism of order 2 and Whittaker vectors

For an arbitrary positive integer T we introduce a notion of a (V, T )-module over a vertex algebra V , which is a generalization of a twisted V -module. Under some conditions on V , we construct an associative algebra Am(V ) for m ∈ (1/T )N and an A T m(V )-A T n (V )bimodule An,m(V ) for n,m ∈ (1/T )N and we establish a one-to-one correspondence between the set of isomorphism classes of simple left A0 (V )-modules and that of simple (1/T )N-graded (V, T )-modules. 2010 Mathematics Subject Classification. Primary 17B69; Secondary 17B68.

A generalization of intertwining operators for vertex operator algebras

Abstract Let K be a differential field over C with derivation D, G a finite linear automorphism group over K which preserves D, and K G the fixed point subfield of K under the action of G. We show that every finite-dimensional vertex algebra K G -module is contained in some twisted vertex algebra K-module.

Finite-dimensional vertex algebra modules over fixed point commutative subalgebras

Let

Z3 symmetry and W3 algebra in lattice vertex operator algebras

M(1)

The fixed point subalgebra of a lattice vertex operator algebra by an automorphism of order three

be the vertex operator algebra with the Virasoro element

Representations of a fixed-point subalgebra of a class of lattice vertex operator algebras by an automorphism of order three

\omega