## Automorphism groups of hyperbolic lattices.(English)Zbl 1377.11079

From the text: Based on the concept of dual cones introduced by J. Opgenorth [Exp. Math. 10, No.4, 599–608 (2001; Zbl 1007.20046)] we give an algorithm to compute a generating system of the group of automorphisms of an integral lattice endowed with a hyperbolic bilinear form.
The paper will be organized as follows: In Section 2 we recall the basic definitions and key results about dual cones from the paper cited above which give a general method to determine generating systems of discontinuous groups acting on dual cones. The application of the results in Section 2 on hyperbolic lattices as well as a quite powerful way to shorten the calculation time is given in Section 3. In Section 4 we analyse the scope and running time of our algorithm and give some examples. These were calculated using the computer algebra system Magma. The source code for the necessary Magma-package AutHyp.m as well as a short description of the included intrinsics is available via the author’s homepage http://www.mi.uni-koeln.de/~mmertens.

### MSC:

 11H56 Automorphism groups of lattices

Zbl 1007.20046

### Software:

CARAT; Magma; AutHyp
Full Text:

### References:

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