Publication Date:
2020-09-18
Description:
We explore whether a root lattice may be similar to the lattice [Formula: see text] of integers of a number field [Formula: see text] endowed with the inner product [Formula: see text], where [Formula: see text] is an involution of [Formula: see text]. We classify all pairs [Formula: see text], [Formula: see text] such that [Formula: see text] is similar to either an even root lattice or the root lattice [Formula: see text]. We also classify all pairs [Formula: see text], [Formula: see text] such that [Formula: see text] is a root lattice. In addition to this, we show that [Formula: see text] is never similar to a positive-definite even unimodular lattice of rank [Formula: see text], in particular, [Formula: see text] 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 [Formula: see text].
Print ISSN:
1664-3607
Electronic ISSN:
1664-3615
Topics:
Mathematics
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