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 determines the one of all partial dual lattices of . 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.
Cite
@article{arxiv.1910.06587,
title = {Automorphisms of modular lattices},
author = {Gabriele Nebe},
journal= {arXiv preprint arXiv:1910.06587},
year = {2019}
}