Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras

2024/02/21 by Chen, Hsian-Yang, Lam, Ching Hung
#17B69 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2402.13621

Abstract

We continue our study of cyclic orbifolds of lattice vertex operator algebras and their full automorphism groups. We consider some special isometry g∈ O(L) such that gⁱ is fixed point free on L for any 1≤ i≤ |g|-1. We show that when L₂=∅ and gⁱ is fixed point free on L for any 1≤ i≤ |g|-1, V_L^g has extra automorphisms implies either (1) the order of g is a prime or (2) L is isometric to the Leech lattice or some coinvariant sublattices of the Leech lattice.

Related

• Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras
• Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries
• Fourvolutions and automorphism groups of orbifold lattice vertex operator algebras
• Automorphism groups of certain orbifold vertex operator algebras arising from coinvariant lattices associated with the Leech lattice
• Rank one lattice type vertex operator algebras and their automorphism groups