Gabriele Nebe

RWTH Aachen University

Automorphisms of extremal modular lattices

Heilbronn Number Theory Seminar

7th October 2020, 4:00 pm – 5:00 pm

The study of automorphisms of extremal lattices was motivated by similar research for binary self-dual codes. It started by considering extremal even unimodular lattices in dimensions which are multiples of 24. We know six such lattices, the Leech lattice in dimension 24, four lattices of dimension 48 and, since 2010, also one extremal lattice in dimension 72. One of the 48-dimensional lattices was found by a computer search for lattices with a certain automorphism of order 5.

In his thesis Michael Jürgens extended the theory to automorphisms of modular lattices, aiming in the construction of an extremal 3-modular lattice in dimension 36. In the talk I will present new methods suitable for non unimodular lattices and results partly obtained in joint work with Dr. Markus Kirschmer.

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