Characterization of Self Dual Lattices in R, R2 and R3

Comlan de Souza; David W. Kammler

doi:10.4236/am.2014.510137

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Applied Mathematics > Vol.5 No.10, June 2014

Characterization of Self Dual Lattices in R, R₂ and R₃ ()

Department of Mathematics, California State University at Fresno, Fresno, USA.
Department of Mathematics, Southern Illinois University at Carbondale, Carbondale, USA.

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.

Keywords

Self Dual Lattice

Share and Cite:

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

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[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.