English

Automorphisms of modular lattices

Number Theory 2019-10-16 v1

Abstract

The methods to classify extremal unimodular lattices with given automorphisms are extended to the situation of modular lattices. A slightly more general notion than the type from the PhD thesis of Michael Juergens is the det-type. The det-type of an automorphism on LL determines the one of all partial dual lattices of LL. This easy observation allows to exclude quite a few det-types of automorphisms left open in the above mentioned thesis. Passing to suitable p-maximal lattices, extremal l-modular lattices of composite level 14 and 15 of dimension 12 and the ones of level 6 and dimension 16 are classified.

Keywords

Cite

@article{arxiv.1910.06587,
  title  = {Automorphisms of modular lattices},
  author = {Gabriele Nebe},
  journal= {arXiv preprint arXiv:1910.06587},
  year   = {2019}
}
R2 v1 2026-06-23T11:43:52.658Z