On Indecomposable Definite Unimodular Hermitian Forms

作     者：Zhu Fuzu Department of Mathematics East China Normal University Shanghai, 200062 China 

作者机构：Department of Mathematics East China Normal University Shanghai China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：1994年第10卷第2期

页      面：113-120页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：show On Indecomposable Definite Unimodular Hermitian Forms Math 

摘      要：For any natural numbers m and n≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rank n over the ring of algebraic integers Rm in an imaginary quadratic field (-m1/2). It is proved that for any n （in case m=11, there is one exception n=3） there exist indecomposable definite unimodular normal Hermitian R15(R11- lattices of rank n, and we exhibit representatives for each class. In the exceptional case there are no lattices with the desired properties. The method given in this paper can solve completely the problem of constructing indecomposable definite unimodular normal Hermitian Rm-lattices of any rank n for each m.