Explicit examples of unimodular lattices with the trivial automorphism group. (English) Zbl 0735.11026

Algebra and topology, Proc. 5th Math. Workshop, Taejon/Korea 1990, Proc. KIT Math. Workshop 5, 91-95 (1990).
[For the entire collection see Zbl 0727.00012.]
It has been shown by E. Bannai [Mem. Am. Math. Soc. 429 (1990; Zbl 0702.11037)] that for \(n>42\) (resp. \(>136\)) there must exist odd (resp. even) unimodular lattices in \(n\)-dimensional Euclidean space whose group of isometric automorphisms consists only of \(\pm\text{id}\). In the present paper explicit examples of such lattices are given, namely two odd ones of rank 36 and 40, and an even one of rank 64. The construction uses Kneser’s neighbour method.


11H56 Automorphism groups of lattices
11E57 Classical groups