Positive Definite Unimodular Lattices with Trivial Automorphism Groups

Download or read book Positive Definite Unimodular Lattices with Trivial Automorphism Groups written by Etsuko Bannai and published by American Mathematical Soc.. This book was released on 1990 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: The existence of lattices with trivial automorphism group was shown by O'Meara, who gave an algorithm to construct such a lattice starting from any given lattice. In this process, the discriminants of the lattices increase in each step. Biermann proved the existence of a lattice with trivial automorphism group in every genus of positive definite integral lattices of any dimension with sufficiently large discriminant. In his proof the fact that the discriminant is very large is crucial. We are, instead, interested in lattices with small discriminant.