TY - JOUR

T1 - Root lattices in number fields

AU - Popov, Vladimir L.

AU - Zarhin, Yuri G.

N1 - Publisher Copyright:
© 2021 The Author(s).

PY - 2021/12/1

Y1 - 2021/12/1

N2 - We explore whether a root lattice may be similar to the lattice of integers of a number field K endowed with the inner product (x,y):= TraceK/a,s(x a(y)), where is an involution of K. We classify all pairs K, such that is similar to either an even root lattice or the root lattice a,[K:a,s]. We also classify all pairs K, such that is a root lattice. In addition to this, we show that is never similar to a positive-definite even unimodular lattice of rank 48, in particular, is not similar to the Leech lattice. In Appendix B, we give a general cyclicity criterion for the primary components of the discriminant group of O.

AB - We explore whether a root lattice may be similar to the lattice of integers of a number field K endowed with the inner product (x,y):= TraceK/a,s(x a(y)), where is an involution of K. We classify all pairs K, such that is similar to either an even root lattice or the root lattice a,[K:a,s]. We also classify all pairs K, such that is a root lattice. In addition to this, we show that is never similar to a positive-definite even unimodular lattice of rank 48, in particular, is not similar to the Leech lattice. In Appendix B, we give a general cyclicity criterion for the primary components of the discriminant group of O.

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U2 - 10.1142/S1664360720500216

DO - 10.1142/S1664360720500216

M3 - Article

AN - SCOPUS:85094136341

SN - 1664-3607

VL - 11

JO - Bulletin of Mathematical Sciences

JF - Bulletin of Mathematical Sciences

IS - 3

M1 - 2050021

ER -