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

Kenichiro Tanabe and Hiromichi Yamada

Vol. 230 (2007), No. 2, 469–510

DOI: 10.2140/pjm.2007.230.469

Abstract

We study the subalgebra of the lattice vertex operator algebra V _{A 2} consisting of the fixed points of an automorphism which is induced from an order-three isometry of the root lattice A₂. We classify the simple modules for the subalgebra. The rationality and the C₂-cofiniteness are also established.

Keywords

vertex operator algebra, orbifold, W₃ algebra

Mathematical Subject Classification 2000

Primary: 17B69

Secondary: 17B68

Milestones

Received: 11 August 2005

Revised: 11 January 2006

Published: 1 April 2007