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Non-rigidity Degree of a Lattice and Rigid Lattices

✍ Scribed by Evgenii Baranovskii; Viatcheslav Grishukhin

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
141 KB
Volume
22
Category
Article
ISSN
0195-6698

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✦ Synopsis

Voronoi defines a partition of the cone of positive semidefinite n-ary forms

2 , where n is the number of variables and dimension of the corresponding lattice. We define a non-rigidity degree of a lattice as the dimension of the L-type domain containing the lattice. We prove that the non-rigidity degree of a lattice equals the corank of a system of equalities connecting norms of minimal vectors of cosets of 2L in L. A lattice of non-rigidity degree 1 is called rigid. A lattice is rigid if any of its sufficiently small deformations distinct from a homothety changes its L-type. Using the list of 84 zone-contracted Voronoi polytopes in R 5 given by Engel [8], we give a complete list of seven fivedimensional rigid lattices.

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