Smooth lattices over quadratic integers

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Quaternion order

Quadratic integers

Quadratic space

Smooth lattice

Quadratic space

Smooth lattice

Quadratic integers

Quaternion order

Matematik

Publication and Content Type

art (subject category)

ref (subject category)