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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 matrix algebra...

space. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by H . {\displaystyle \mathbb {H} .} Quaternions are not a...

In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form q = a + b i + c...

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

of versors with quaternion multiplication forms a group, and the set of versors is a 3-sphere in the 4-dimensional quaternion algebra. Hamilton denoted...

These relations, discovered by W. R. Hamilton, also generate the quaternions as an algebra over the real numbers. Another presentation of Q8 is Q 8 = ⟨ a...

In mathematics, a Hurwitz quaternion (or Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (halves of odd...

simple algebra A then dimF S divides dimF A. Every 4-dimensional central simple algebra over a field F is isomorphic to a quaternion algebra; in fact...

structure of a distinguished subspace. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems...

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

quaternions of norm 1 in a suitable order in a quaternion algebra. More specifically, the triangle group is the quotient of the group of quaternions by...

chooses a suitable Hurwitz quaternion order Q H u r {\displaystyle {\mathcal {Q}}_{\mathrm {Hur} }} in the quaternion algebra, Γ(I) is then the group of...

as Cayley–Dickson algebras, for example complex numbers, quaternions, and octonions. These examples are useful composition algebras frequently applied...

the dual quaternion algebra to 2D geometry. At this present time, the article is focused on a 4-dimensional subalgebra of the dual quaternions which we...

algebra of (real) quaternions. In other words, the biquaternions are just the complexification of the quaternions. Viewed as a complex algebra, the biquaternions...

"geometric algebras"). Clifford defined the Clifford algebra and its product as a unification of the Grassmann algebra and Hamilton's quaternion algebra. Adding...

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three...

product depends on selection of a γ from k. Given q and Q from a quaternion algebra over k, the octonion is written q + Qe. Another octonion may be written...

functional analysis, Banach *-algebras and C*-algebras are special types of Banach algebras with involutions. In a quaternion algebra, an (anti-)involution is...

quaternion algebra over R, which was an experimental algebra before the adoption of Minkowski space for special relativity. More classes of algebras:...