ON AUTOMORPHISMS OF EXTREMAL EVEN UNIMODULAR LATTICES-Reference-Cited by-同舟云学术

ON AUTOMORPHISMS OF EXTREMAL EVEN UNIMODULAR LATTICES

Published:2013-12 Issue:08 Volume:09 Page:1933-1959
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

NEBE GABRIELE¹

Affiliation:

1. Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen, Germany

Abstract

The automorphism groups of the three known extremal even unimodular lattices of dimension 48 and the one of dimension 72 are determined using the classification of finite simple groups. Restrictions on the possible automorphisms of 48-dimensional extremal lattices are obtained. We classify all extremal lattices of dimension 48 having an automorphism of order m with φ(m) > 24. In particular the lattice P48nis the unique extremal 48-dimensional lattice that arises as an ideal lattice over a cyclotomic number field.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179304211350067X

Reference24 articles.

1. Unimodular hermitian lattices in dimension 13

2. Unimodular lattices in dimensions 14 and 15 over the Eisenstein integers

3. Applications of Coding Theory to the Construction of Modular Lattices

4. C. Bachoc and B. Venkov, Réseaux euclidiens, designs sphériques et formes modulaires, Monographies de L'Enseignement Mathématique (Enseignement Mathematique, Geneva, 2001) pp. 87–111.

5. Definite unimodular lattices having an automorphism of given characteristic polynomial

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Prime Order Isometries of Unimodular Lattices and Automorphisms of IHS Manifolds;International Mathematics Research Notices;2022-10-13

2. Non-abelian orbifolds of lattice vertex operator algebras;Journal of Algebra;2021-11

3. Automorphisms of modular lattices;Journal of Pure and Applied Algebra;2021-07

4. Binary Hermitian Lattices over Number Fields;Experimental Mathematics;2019-06-07

5. Automorphisms of extremal unimodular lattices in dimension 72;Journal of Number Theory;2016-04