A note on unimodular lattices with trivial automorphism groups

作者：Wang, Jin^*

来源：Discrete Mathematics, 2017, 340(4): 763-765.

DOI：10.1016/j.disc.2016.11.023

• Unimodular lattice
• Automorphism group
• Tri-diagonal matrix

In this paper, we give a simple construction method of positive definite unimodular lattices with trivial automorphism groups (i.e., the tri-diagonal matrix method), and obtain odd positive definite unimodular lattices of dimensions 29 <= n <= 42 and even positive definite unimodular lattices of dimensions n = 32, 40 with trivial automorphism groups. Combining these with Bannai's and Bacher and Venkov's results we obtain that there exists a unimodular lattice with a trivial automorphism group if and only if the dimension n > 28.

• 出版日期2017-4
• 单位中原工学院