Computer Science Journal of Moldova (Sep 2021)
Cube-root-subgroups of SL2 over imaginary quadratic integers
Abstract
All cube roots of the identity in the special linear group of $2\times 2$-matrices with entries in the ring of integers in $\mathbb Q[\sqrt{d}]$ 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.