Lattices: Automorphisms

• Automorphism group of a lattice
• Subgroup of the automorphism group of a lattice fixing specified bilinear forms
• Determination of whether two lattices are isometric
• Determination of whether two lattices are isometric in such a way that specified bilinear forms are fixed

The computation of the automorphism group of a lattice and the testing of lattices for isometry is performed using the AUTO and ISOM programs of Bernd Souvignier. The automorphism group Co₀ of the 24-dimensional Leech lattice $\Lambda_{24}$ is found in 175 seconds.