Smooth lattices over quadratic integers
Artikel i vetenskaplig tidskrift, 2008

We construct lattices with quadratic structure over the integers in quadratic number fields having the property that the rank of the quadratic structure is constant and equal to the rank of the lattice in all reductions modulo maximal ideals. We characterize the case in which such lattices are free. The construction gives a representative of the genus of such lattices as an orthogonal sum of "standard" pieces of ranks 1-4 and covers the case of the discriminant of the real quadratic number field congruent to 1 modulo 8 for which a general construction was not known. © 2007 Springer-Verlag.

Quadratic integers

Quadratic space

Smooth lattice

Quaternion order


Juliusz Brzezinski

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Håkan Granath

Karlstads universitet

Stefan Lemurell

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. 258 161-184