Characterization of Self Dual Lattices in R, R2 and R3

DOI: 10.4236/am.2014.510137   PDF   HTML   XML   4,379 Downloads   5,100 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.


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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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