In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They...

In mathematics, a quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a...

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton...

polynomial f ∈ k[x1, ..., xn]. There is a hyperboloid of idempotents in the split-quaternion ring.[citation needed] A partial list of important types of idempotents...

In mathematics, a versor is a quaternion of norm one (a unit quaternion). Each versor has the form q = exp ⁡ ( a r ) = cos ⁡ a + r sin ⁡ a , r 2 = − 1...

In group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset {...

spins. Clifford introduced the use of split-complex numbers as coefficients in a quaternion algebra now called split-biquaternions. He called its elements...

In mathematics, the dual quaternions are an 8-dimensional real algebra isomorphic to the tensor product of the quaternions and the dual numbers. Thus...

just as the quaternion algebra H can be viewed as a union of complex planes, so the hyperbolic quaternion algebra is a pencil of planes of split-complex numbers...

original Cayley–Dickson construction to the split-complexes also results in the split-quaternions and then the split-octonions. Albert (1942, p. 171) gave a...