Octoniones. Construcción, geometría y aplicaciones
- Autores: Andrés Ricardo Moreno Garzón, Diana Andrea Toquica Arenas
- Localización: Boletín de matemáticas, ISSN 0120-0380, ISSN-e 2357-6529, Vol. 26, Nº. 2, 2019, págs. 119-144
- Idioma: español
- Títulos paralelos:
- Octonions. Construction, geometry and applications
- Enlaces
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Resumen
- español
Los octoniones son el álgebra de división normada con mayor dimensión. Su construcción abarca propiedades algebraicas, su geometría y la relación con ramas de la matemática como el álgebra abstracta y la geometría diferencial. En este trabajo se mostrarán las diferentes construcciones realizadas a lo largo de la historia, así como la geometría de este conjunto de la cual surgen relaciones con la física en la relatividad especial y la física cuántica.
- English
Octonions are the largest normed division algebra. Its construction covers the algebraic properties, its geometry and the relationship with branches of mathematic such as abstract algebra and differential geometry. In this work, we will stydy some made constructions through history, as well as the geometry of this set from which relationships with physics arise in special relativity and quantum physics
- español
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Referencias bibliográficas
- J. C. Baez, The octonions, Bulletin of American Mathematical Society 39 (2002), 145-205.
- B. A. Bernevig, J. Hu, N. Toumbas, and S. Ch. Zhang, Eight-Dimensional Quantum Hall Effect and Octonions, Physical Review Letters 96 (2006),...
- L. Borsten, D. Dahanayake, M. J. Duff, H. Ebrahima, and W. Rubens, Black holes, qubits and octonions, Elsevier B.V. Physics Reports (2009).
- J. H. Conway and D. A. Smith, On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry, 1 ed., vol. 1, Sales, and Customer Service...
- G. M. Dixon, Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics, 1 ed., Mathematics and Its Applications...
- T. Dray and C. A. Manogue, The Geometry of the Octonions, 1 ed., vol. 1, World Scientific Publishing, 2015.
- J. Koplinger, Dirac equation on hyperbolic octonions, Applied Mathematics and Computation 182 (2006), no. 1, 443-446.
- O. Lezama, Algebra Lineal, Cuadernos de clase, 2018.
- P. Lounesto, Clifford Algebras and Spinors, 2 ed., vol. 1, Cambridge University Press, 2001.
- D. W. Lyons, An Elementary Introduction to the Hopf Fibration, Lebanon Valley College 76 (2003).
- Quanta Magazine, The peculiar math that could underlie the laws of nature.
- Mathworld, Projective plane.
- Encyclopedy of Mathematics, Cayley-dickson algebra.
- Y. Tian, Matrix representations of octonions and their applications, Advances in Applied Clifford Algebras, Birkhäuser Basel 10 (2000), no....
- Wikipedia, Dirac equation.
- Wikipedia, Feynman diagram.
- Wikpedia, Octonions.
