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^{n}} with circles as fibers, and there are also real, quaternionic, and octonionic versions of these fibrations. In particular, the Hopf fibration belongs...

\theta +u\sin \theta )=\|o\|e^{u\theta }} thus providing a polar form. Octonionic multiplication is neither commutative: e i e j = − e j e i ≠ e j e i {\displaystyle...

In mathematics, the Cayley plane (or octonionic projective plane) P2(O) is a projective plane over the octonions. The Cayley plane was discovered in 1933...

the isometry group of a 16-dimensional Riemannian manifold known as the octonionic projective plane OP2. This can be seen systematically using a construction...

Profile, a Bluetooth communications protocol based on the OBEX protocol Octonionic projective plane, or Cayley plane, a projective plane over the octonions...

The Eilenberg–Niven theorem can also be generalized to octonions: all octonionic polynomials with a unique monomial of highest degree have at least one...

ISBN 0-8247-2669-3. Rafał Abłamowicz; Pertti Lounesto; Josep M. Parra (1996). "§ Four octonionic basis numberings". Clifford algebras with numeric and symbolic computations...

native split-octonion arithmetic. Supersymmetric quantum mechanics has an octonionic extension. The Zorn-based split-octonion algebra can be used in modeling...

but this fails since octonion multiplication is nonassociative. The octonionic structure does give S7 one important property: parallelizability. It turns...

the first exotic spheres were discovered. 8-sphere Homeomorphic to the octonionic projective line ⁠ O P 1 {\displaystyle \mathbf {OP} ^{1}} ⁠. 23-sphere...

illustration of space-time algebra spinors in Cl[0] (1,3)(R) under the octonionic product as a Fano plane. A nonzero vector ⁠ a {\displaystyle a} ⁠ is a...

\mathbf {O} P^{2}} (dimension 16, octonionic projective plane) and the analogous Rosenfeld projective planes (the bi-octonionic projective plane in dimension...

Jordan algebra of Clifford type. The Jordan algebra of 3×3 self-adjoint octonionic matrices, as above (an exceptional Jordan algebra called the Albert algebra)...

groups, and the exceptional Lie groups, which the book interprets as octonionic variants of classical Lie groups. The third part applies the octonions...

worked on attempting to obtain the Standard Model of particle physics from octonionic constructions. In her 2018 paper "SU(3)C × SU(2)L × U(1)Y (× U(1)X) as...

Following Ruth Moufang's discovery in 1933 of the Cayley projective plane or "octonionic projective plane" P2(O), whose symmetry group is the exceptional Lie group...

(20 October 2005). "The Chevalley group G2(2) of order 12096 and the octonionic root system of E7". Linear Algebra and Its Applications. 422 (2–3): 808–823...

_{HP^{2}}[u^{2}]\\&=\epsilon *1=\epsilon \end{aligned}}} Example (elliptic genus for octonionic projective plane, or Cayley plane): Φ e l l ( O P 2 ) = ∫ O P 2 1 113400...

is the group of collineations (line-preserving transformations) of the octonionic projective plane OP2. It is also the group of determinant-preserving linear...