2026-10-18T23:56:44Zhttps://ebyu-rdlopen.rawdatalibrary.net/oai/request

oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/105472026-10-18T20:25:44Zopenairedrivercom_ebyu_10000col_ebyu_10001

On Fibonacci and Lucas Quasi-quaternions: Theoretical insights and graphical representationsUysal, MineKuloğlu, BaharÖzkan, EnginCassini identityFibonacci numbersgraphical representationsmatrix representationsquasi-quaternionQuaternionIn this paper, we introduce Fibonacci and Lucas quasi-quaternions by combining classical number sequences with the structure of quasi-quaternion algebra. We investigate their fundamental algebraic properties, including real and imaginary parts, conjugates, norms, and recurrence relations. We establish Binet-type formulas, generating functions, and sum formulas for these sequences in the quasi-quaternionic setting. In addition, we derive several classical identities, such as the Cassini, Catalan, d’Ocagne, Vajda, and Honsberger identities, adapted to Fibonacci and Lucas quasi-quaternions. Furthermore, we present matrix representations of these structures and obtain explicit expressions for the powers of the associated matrices. We also consider De Moivre-type formulas in the quasi-quaternion framework and analyze the behavior of these sequences under repeated operations. The graphical representations complement the theoretical results by illustrating the structural and asymptotic behavior of these quasi-quaternionic sequences. © 2026 by the authors.Ptolemy Scientific Research Press2026Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/10547https://doi.org/10.30538/oms2026.03082616-4906enOpen Journal of Mathematical Sciencesinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/10547