Recurrence relations over division algebras
Rings and Algebras
2025-09-23 v1
Abstract
We generalize the solution of linear recurrence relations from fields to central division algebras, adapting the standard tools of companion matrices and characteristic polynomials to the non-commutative setting. We then solve linear recurrences of order 2 over octonion division algebras.
Cite
@article{arxiv.2509.17826,
title = {Recurrence relations over division algebras},
author = {Adam Chapman and Solomon Vishkautsan},
journal= {arXiv preprint arXiv:2509.17826},
year = {2025}
}
Comments
20 pages