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On indecomposable definite unimodular hermitian forms

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Abstract

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.

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References

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, 200062, Shanghai, China

    Zhu Fuzu

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  1. Zhu Fuzu
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Dedicated to the memory of Prof. Lee Hwa-Chung.

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Fuzu, Z. On indecomposable definite unimodular hermitian forms. Acta Mathematica Sinica 10, 113–120 (1994). https://doi.org/10.1007/BF02580417

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  • DOI: https://doi.org/10.1007/BF02580417

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