A New Polar Representation and Identities for Split Leonardo Quaternions

ABSTRACT In this study, we define split Leonardo quaternion sequences with components involving Leonardo numbers. We give fundamental properties and identities associated with split Leonardo quaternions, such as Binet's formula, as well as identities attributed to Catalan, Cassini, and d'Ocagne. Furthermore, we introduce an innovative concept: polar representation for these split quaternions using Cayley Dickson's notation. This alternative representation provides a new perspective on the structure of split Leonardo quaternions and give a deeper understanding of their geometric interpretations and transformations.