CONSTRUCTION OF INDECOMPOSABLE POSITIVE DEFINITE UNIMODULAR HERMITIAN FORMS

摘要

This paper gives a method to construct indecomposable positive definite unimodular Hermitian (?)-lattices of any rank n with m(?)3 (mod 4). It is proved that we can construct: (i) for any natural number n, an indecomposable positive definite normal unimodular (?)-(resp. (?)-lattice of rank n, except n=2, 3, 4,5 (resp. n=2, 3) (in the exceptional cases there are no lattices with the desired properties), and (ⅱ) for any n=4k(resp. n=2k), an indecompoaable positive definite even unimodular (?) lattice of rank n.