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Octonions

TODO ...

http://www.hyperfract.com

 

General:

• Ubiquitous Octonion - H. Joyce

• The missing Link - I. Stewart

• Octonions and other Division Algebras - G. Dixon

• This week's finds in mathematical physics (week 104) - J. Baez

• Octonions and Sedenions

• The Octonions - J. C. Baez

• Constructions for octonion and exceptional Jordan algebras - L.J. Rylands, D.E. Taylor

• Exceptional Projective Geometries and Internal Symmetries - S. Catto

• Matrix Representations of Octonions and Generalisations - J. Daboul, J. Delbourgo

• Quaternionic Spin - T. Dray, C. A.Manogue

• Octonionic Hermitian Matrices with non-real Eigenvalues

• Real vector product algebras - E. Darpö

• The Geometry of the Octonions - T. Dray

• The weird and wonderful world of the octonions - R. A. Wilson

 

Mathematics:

• The Cauchy Integral Formulas on the Octonions - X. Li, L. Peng

• Octonions and Triality - P. Lounesto

• Octonions and Exceptional Groups? - W. Lin

• Multi dimensional vector product - Z.K. Silagadze

• Exceptional Structures in Mathematics and Physics and the Role of the Octonions - F. Toppan

• Seven-Spheres from Octonions - J. Lukierski, P. Minnaert

• Finding Octonionic Eigenvectors Using Mathematica - T. Dray, C. A. Manogue

• Octonions: E8 Lattice to ?16 - G. Dixon

• On the Structure of the Split Octonion Algebra - L. P. Nash

• Matrix Representations of Octonions and their Applications - Y. Tian

• Matrix Representation of Octonions and Generalizations - J. Daboul, R. Delbourgo

• Octonions, simple Moufang Loops and Triality - G. P. Nagy, P. Vojtechovsky

• Compact Manifolds with Holonomy Spin(7) - C. Taylor

• Octonions, G2 and generalized Lie 3-algebras - M. Yamazaki

• Manifolds with G2 Holonomy - J. D. Olson

• S7 and ^S7 - M. Cederwall, C. R. Preitschopf

• Finding Octonionic Eigenvectors Using Mathematica - T. Dray, C. A. Manogue

Analysis

• Funzioni regolari nell'algebra di Cayley - P. Dentoni, M. Sce

• The Theory of Functions of an Octonion Variable - K. Imaeda, M. Imaeda

Octonions & Clifford Algebras

• Octonionic representations of Clifford algebras and triality - J. Schray, C. A. Minogue

• Clifford algebra-parametrized octonions and generalizations - R. d. Rocha, J. Vaz Jr.

 

Physics:

• About Nonassociativity in Physics and Cayley Graves' Octonions - L. Sorgsepp, J. Löhmus

• Octonionic Geometry - M. Gogberashvili

• Observable Algebra - M. Gogberashvili

• Superalgebras of (split-) division algebras and the split octonionic M-theory in (6,5)-signature - Z. Kuznetsova, F. Toppan

Electrodynamics

• Octonionic Electrodynamics - M. Gogberashvili

• Feynman's Derivation of Maxwell Equations - Z.K. Silagadze

Quantum Mechanics

• Moufang Plane and Octonionic Quantum Mechanics - M. Günaydin, C. Piron, H. Ruegg

• Octonic relativistic quantum mechanics I. The second-order equations

• Toy models of a non-associative quantum mechanics - V. Dzhunushaliev

• Octonionic Versions of Dirac Equations - M. Gogberashvili

Gauge Theory

• On a construction of self-dual gauge fields in seven dimensions - E. K. Loginov, A. N. Grishkov

• An Octonionic Gauge Theory - C. C. Lassig, G. C. Joshi

 

Relativity

• On the Noncommutative and Nonassociative Geometry of Octonionic Spacetime, Modified Dispersion Relations and Grand Unification - C. Castro

• Octonionic Gravity, Grand-Unification and Modified Dispersion Relations - C. Castro

 

Links:

• Octonions - Wikipedia

 

Not classified (yet):

Nonassociative Algebras - M. R. Bremner, L. I. Murakami, I. P. Shestakov

Non-associative Gauge Theory - T. Ootsuka, E. Tanaka, E. Loginov

Triple Products and Yang–Baxter Equation (I): Octonionic and Quaternionic Triple Systems

Triple Products and Yang-Baxter Equation (II): Orthogonal and Symplectic Ternary Systems

Finite Invariance of Cayley Calibration Form - Y. Song

On Malcev Algebras - T. S. Ravisankar

Vertex Functions and Generalized Normal-Ordering by Triple Systems - B. Fauser

Moufang's Theorem

Pseudo-Riemannian Metrics with Parallel Spinor Fields and vanishing Ricci Tensor - R. L. Bryant

Glimpses of the Octonions and Quaternions History and Today's Applications in Quantum Physics - A. K. Kwasnewski

Non-associative Gauge Theory - T. Ootsuka, E. Tanaka, E. Loginov

 

Related topics: Quaternions, Sedenions, Geometric Algebra, Hypercomplex Numbers, Nonassociative Algebras and Geometry