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Unimodular lattices in dimensions 14 and 15 over the Eisenstein integers


Authors: Kanat Abdukhalikov and Rudolf Scharlau
Journal: Math. Comp. 78 (2009), 387-403
MSC (2000): Primary 11H06, 11H56; Secondary 11E39, 11H71, 11F11
DOI: https://doi.org/10.1090/S0025-5718-08-02131-5
Published electronically: May 16, 2008
MathSciNet review: 2448712
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Abstract: All indecomposable unimodular hermitian lattices in dimensions 14 and 15 over the ring of integers in $ \mathbb{Q}(\sqrt{-3})$ are determined. Precisely one lattice in dimension 14 and two lattices in dimension 15 have minimal norm 3.


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Additional Information

Kanat Abdukhalikov
Affiliation: Institute of Mathematics, 125 Pushkin Str, 050010, Kazakhstan
Email: abdukhalikov@math.kz

Rudolf Scharlau
Affiliation: Department of Mathematics, University of Dortmund, 44221 Dortmund, Germany
Email: Rudolf.Scharlau@math.uni-dortmund.de

DOI: https://doi.org/10.1090/S0025-5718-08-02131-5
Keywords: Integral lattice, hermitian lattice, extremal lattice, unimodular lattice, root system
Received by editor(s): October 19, 2007
Received by editor(s) in revised form: January 2, 2008
Published electronically: May 16, 2008
Additional Notes: The first author was supported by the Alexander von Humboldt Foundation.
Article copyright: © Copyright 2008 American Mathematical Society