  In this paper, we connect two well established theories, the Fibonacci
numbers and the Jordan algebras. We give a series of matrices, from literature,
used to obtain recurrence relations of second-order and polynomial sequences.
We also give some identities known in special Jordan Algebras. The matrices
play a bridge role between both theories. The mentioned matrices connect both
areas of mathematics, special Jordan algebras and recurrence relations, to
obtain new identities and classic identities in Fibonacci numbers, Lucas
numbers, Pell numbers, binomial transform, tribonacci numbers, and polynomial
sequences among others. The list of identities in this paper contains just a
few examples of many that the reader can find using this technique.
