Clifford algebras | Historical treatment of quaternions

Split-biquaternion

In mathematics, a split-biquaternion is a hypercomplex number of the form where w, x, y, and z are split-complex numbers and i, j, and k multiply as in the quaternion group. Since each coefficient w, x, y, z spans two real dimensions, the split-biquaternion is an element of an eight-dimensional vector space. Considering that it carries a multiplication, this vector space is an algebra over the real field, or an algebra over a ring where the split-complex numbers form the ring. This algebra was introduced by William Kingdon Clifford in an 1873 article for the London Mathematical Society. It has been repeatedly noted in mathematical literature since then, variously as a deviation in terminology, an illustration of the tensor product of algebras, and as an illustration of the direct sum of algebras.The split-biquaternions have been identified in various ways by algebraists; see below. (Wikipedia).

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Related pages

Clifford algebra | Split-complex number | Vector space | Coefficient | Division ring | Direct sum of modules | Hypercomplex number | Dimension | Algebra over a field | William Rowan Hamilton | Free module | Eight-dimensional space | Group ring | Mathematics | Biquaternion | Real number | Tensor product of algebras | Ring theory | Geometric algebra | Basis (linear algebra) | Split-octonion | Quaternion group