On Leonardo, Leonardo–Lucas and modified Leonardo elliptic quaternions and their matrix representations

In this paper, we present a new class of elliptic quaternions that incorporate Leonardo, Leonardo–Lucas and modified Leonardo numbers into their components. We explore some fundamental properties associated with these numbers. In particular, we obtain recurrence relations, generating function, Binet formula of these sequences and by using Binet formula we derive Vajda, Cassini, Catalan and d’Ocagne identities. Lastly, we investigate two different matrix representations of these numbers.