Cube-root-subgroups of SL2 over imaginary quadratic integers
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...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova
2021-09-01
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| Series: | Computer Science Journal of Moldova |
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| Online Access: | http://www.math.md/files/csjm/v29-n2/v29-n2-(pp227-240).pdf |
| Summary: | 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. |
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| ISSN: | 1561-4042 |