Pell and Pell-Lucas Hybrid Quaternions

Abstract

In this paper, we investigate Pell and Pell-Lucas numbers what new properties we can obtain by working on a new number system-hybrid quaternions. Firstly, we present some new identities of Pell and Pell-Lucas numbers and quaternions. Then, with the help of these identities and previously known identities, we get new identities on Pell and Pell-Lucas hybrid quaternions, including Binet's and Cassini's identities.