Abstract
Root lattices are orthogonal sums of irreducible lattices which are either the lattice ℤ or the lattices of norm 2 consisting of two infinite families 𝔸n, 𝔻 n and three exceptional lattices 𝔼6, 𝔼7, 𝔼8. They play a crucial rôle in Coxeter’s classification of groups generated by reflections (the roots are then vectors which are orthogonal to the hyperplanes defining the reflections, whence the name given to these lattices). Those which are irreducible are extreme. Moreover, they are involved in numerous constructions of extreme lattices. Finally, the Hermite constant is attained on root lattices in dimensions up to 8 (but in no higher dimension).
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© 2003 Springer-Verlag Berlin Heidelberg
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Martinet, J. (2003). Root Lattices. In: Perfect Lattices in Euclidean Spaces. Grundlehren der mathematischen Wissenschaften, vol 327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05167-2_4
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DOI: https://doi.org/10.1007/978-3-662-05167-2_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07921-4
Online ISBN: 978-3-662-05167-2
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