Smooth lattices over quadratic integers
Journal article, 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.

Quaternion order

Quadratic integers

Quadratic space

Smooth lattice

Author

Juliusz Brzezinski

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Håkan Granath

Karlstad University

Stefan Lemurell

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Mathematische Zeitschrift

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

Vol. 258 1 161-184

Subject Categories

Mathematics

DOI

10.1007/s00209-007-0166-8

More information

Latest update

5/23/2018