Geodesic
A Generalization of complex, dual and hyperbolic quaternions: hybrid quaternions
Filomat, Tome 37 (2023) no. 25, p. 8441

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DOI

Hybrid numbers are a new non-commutative number system which is a generalization of the complex (i2 = −1), dual (ε2 = 0), and hyperbolic numbers (h2 = 1). In this article, firstly we define a new quaternion system called hybrid quaternions by taking the coefficients of real quaternions as hybrid numbers. This new quaternion system is a combination of complex quaternions (biquaternions), hyperbolic (perplex) quaternions, and dual quaternions, and it can be viewed as a generalization of these quaternion systems. Then, we present the basic properties of hybrid quaternions including fundamental operations, conjugates, inner product, vector product, and norm. Finally, wegive a schematic representation of numbers and quaternions.
DOI : 10.2298/FIL2325441D
Classification : 11R52, 15A63, 15A66
Keywords: Real quaternions, Complex quaternions, Dual quaternions, Hyperbolic quaternions 
Ali Dagdeviren. A Generalization of complex, dual and hyperbolic quaternions: hybrid quaternions. Filomat, Tome 37 (2023) no. 25, p. 8441 . doi: 10.2298/FIL2325441D
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     author = {Ali Dagdeviren},
     title = {A {Generalization} of complex, dual and hyperbolic quaternions: hybrid quaternions},
     journal = {Filomat},
     pages = {8441 },
     year = {2023},
     volume = {37},
     number = {25},
     doi = {10.2298/FIL2325441D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2325441D/}
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