TY - JOUR

T1 - Root lattices in number fields

AU - Popov, Vladimir L.

AU - Zarhin, Yuri G.

N1 - Publisher Copyright:
© 2020 The Author(s).

PY - 2020

Y1 - 2020

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/Q(x.(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 Z[K:Q]. We also classify all pairs K, θ 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.

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/Q(x.(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 Z[K:Q]. We also classify all pairs K, θ 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.

UR - http://www.scopus.com/inward/record.url?scp=85094136341&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85094136341&partnerID=8YFLogxK

U2 - 10.1142/S1664360720500216

DO - 10.1142/S1664360720500216

M3 - Article

AN - SCOPUS:85094136341

JO - Bulletin of Mathematical Sciences

JF - Bulletin of Mathematical Sciences

SN - 1664-3607

M1 - 2050021

ER -