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Mathematics > Quantum Algebra

Title: Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras

Abstract: In this article, we study the automorphism group of the cyclic orbifold of a vertex operator algebra associated with a rootless even lattice for a lift of a fixed-point free isometry of odd prime order $p$. We prove that such a cyclic orbifold contains extra automorphisms, not induced from automorphisms of the lattice vertex operator algebra, if and only if the rootless even lattice can be constructed by Construction B from a code over $\mathbb{Z}_p$ or is isometric to the coinvariant lattice of the Leech lattice associated with a certain isometry of order $p$.
Comments: 35 pages
Subjects: Quantum Algebra (math.QA); Combinatorics (math.CO); Group Theory (math.GR)
MSC classes: 17B69
Cite as: arXiv:2103.08085 [math.QA]
  (or arXiv:2103.08085v1 [math.QA] for this version)

Submission history

From: Hiroki Shimakura [view email]
[v1] Mon, 15 Mar 2021 01:07:22 GMT (33kb)

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