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Characterization of Self Dual Lattices in R, R2 and R3

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DOI: 10.4236/am.2014.510137    4,188 Downloads   4,810 Views  

ABSTRACT

This paper shows that the only self dual lattices in R, R2, R3  are rotations of Z , Z×Z and Z×Z×Z.


Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Souza, C. and Kammler, D. (2014) Characterization of Self Dual Lattices in R, R2 and R3. Applied Mathematics, 5, 1448-1456. doi: 10.4236/am.2014.510137.

References

[1] Kannan, R. (1987) Minkowski’s Convex Body Theorem and Integer Programming. Mathematics of Operations Research, 12, 415-440.
[2] Strang, G. (1976) Linear Algebra and Its Applications. Academic Press, Inc., New York.
[3] Senechal, M. (1995) Quasicrystals and Geometry. Cambridge University Press, New York.
[4] Conway, J.H., Odlyzko, A.M. and Sloane, N.J.A. (1978) Extremal Self-Dual Lattices Exit Only in Dimensions 1 to 8, 12, 14, 15, 23, and 24.

  
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