On indecomposable definite unimodular hermitian forms

For any natural numbersm andn≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rankn over the ring of algebraic integersR _m in an imaginary quadratic field . It is proved that for anyn (in casem=11, there is one exceptionn=3) there exist indecomposable definite unimodular normal HermitianR ₁₅(R ₁₁)-lattices of rankn, 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 HermitianR _m -lattices of any rankn for eachm. Dedicated to the memory of Prof. Lee Hwa-Chung.