Cube-root-subgroups of SL_2 over imaginary quadratic integers

摘要

All cube roots of the identity in the special linear group of 2 x 2-matrices with entries in the ring of integers in Q[root d] are described. These matrices generate subgroups of the third order; it is shown that such subgroups may contain non-elementary matrices in the sense of P. M. Cohn. All this is viewed with respect to possible applications in lattice cryptography.