In abstract algebra, the biquaternions are the numbers w + x i + y j + z k, where w, x, y, and z are complex numbers and the elements of {1, i, j, k} multiply as in the quaternion group. As there are three types of complex number, so there are three types of biquaternion: * (Ordinary) biquaternions when the coefficients are (ordinary) complex numbers * Split-biquaternions when w, x, y, and z are split-complex numbers * Dual quaternions when w, x, y, and z are dual numbers.

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• In abstract algebra, the biquaternions are the numbers w + x i + y j + z k, where w, x, y, and z are complex numbers and the elements of {1, i, j, k} multiply as in the quaternion group. As there are three types of complex number, so there are three types of biquaternion: * (Ordinary) biquaternions when the coefficients are (ordinary) complex numbers * Split-biquaternions when w, x, y, and z are split-complex numbers * Dual quaternions when w, x, y, and z are dual numbers. This article is about the ordinary biquaternions named by William Rowan Hamilton in 1844 (see Proceedings of Royal Irish Academy 1844 & 1850 page 388). Some of the more prominent proponents of these biquaternions include Alexander Macfarlane, Arthur W. Conway, Ludwik Silberstein, and Cornelius Lanczos. As developed below, the unit quasi-sphere of the biquaternions provides a presentation of the Lorentz group, which is the foundation of special relativity. The algebra of biquaternions can be considered as a tensor product C ⊗ H (taken over the reals) where C is the field of complex numbers and H is the algebra of (real) quaternions. In other words, the biquaternions are just the complexification of the (real) quaternions. Viewed as a complex algebra, the biquaternions are isomorphic to the algebra of 2×2 complex matrices M2(C). They can be classified as the Clifford algebra Cℓ2(C) = Cℓ03(C). This is also isomorphic to the Pauli algebra Cℓ3,0(R), and the even part of the spacetime algebra Cℓ01,3(R). (en)
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• 1207070 (xsd:integer)
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http://purl.org/linguistics/gold/hypernym
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• In abstract algebra, the biquaternions are the numbers w + x i + y j + z k, where w, x, y, and z are complex numbers and the elements of {1, i, j, k} multiply as in the quaternion group. As there are three types of complex number, so there are three types of biquaternion: * (Ordinary) biquaternions when the coefficients are (ordinary) complex numbers * Split-biquaternions when w, x, y, and z are split-complex numbers * Dual quaternions when w, x, y, and z are dual numbers. (en)
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• Biquaternion (en)
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