Generalized commutative quaternions of the Fibonacci type. (English) Zbl 1479.11040

Summary: Quaternions are a four-dimensional hypercomplex number system discovered by Hamilton in 1843 and next intensively applied in mathematics, modern physics, computer graphics and other fields. After the discovery of quaternions, modified quaternions were also defined in such a way that commutative property in multiplication is possible. That number system called as commutative quaternions is intensively studied and used for example in signal processing. In this paper we define generalized commutative quaternions and next based on them we define and explore Fibonacci type generalized commutative quaternions.


11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B83 Special sequences and polynomials
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