On the genera of certain integral lattices in ternary quadratic spaces

Abstract

This paper treats certain integral lattices with respect to ternary quadratic forms, which are obtained from the data of a non-zero element and a maximal lattice in a quaternary quadratic space. Such a lattice can be described by means of an order associated with the lattice in the even Clifford algebra of the ternary form. This provides a correspondence between the genus of the lattice and that of the order.