Biquaternium

Biquaternium (Anglice biquaternion) in algebra abstracta est ullus ex numeris  , ubi , et  sunt numeri complexi vel eorum variantes, et elementa  se multiplicant ut in grege quaterniorum et cum eorum coefficientibus commutantur. Sunt tria biquaterniorum genera, quae cum numeris complexis eorumque variantibus congruunt:
 Biquaternia cum coefficientes numeri complexi sint
 Biquaternia fissa cum coefficientes numeri complexi et fissi sint
 Quaternia binaria cum coefficients numeri binarii sint.

Biquaternia ordinaria, a Gulielmo Rowan Hamilton excogitata, annis 1844 et 1850 in Proceedings of the Royal Irish Academy divulgata sunt.Proceedings of the Royal Irish Academy November 1844 (NA) et 1850: 388 in Google Books. Inter gravissimos huius generis biquaterniorum suasores numerantur Arthurus W. Conway, Cornelius Lanczos, Alexander Macfarlane, Ludovicus Silberstein. Quasi-sphaerium, unitas biquaterniorum, gregem Lorentzianum repraesentat, qui fundamenta relativitatis specialis est.

Algebra biquaterniorum putari potest productus tensorum  (supra reales) ubi  est campus numerorum complexorum et  est algebra divisionis quaterniorum realium; quod breviter significat biquaternia esse complexificationem tantum quaterniorum. Biquaternia, cum genus algebrae complexae videantur,  isomorphica ad algebram  matricum complexarum  sunt. Etiam sunt isomorphica ad nonnullas algebras Cliffordianas, inter quas ,D. J. H. Garling, Clifford Algebras: An Introduction (Cantabrigiae: Cambridge University Press, 2011). algebram Paulianam ,Francis and Kosowsky (2005), "The construction of spinors in geometric algebra," Annals of Physics 317: 384–409. Nexus ad commentarium. et par algebrae spatiotemporalis pars .

Notae


Bibliographia

 Buchheim, Arthur. 1885. "A Memoir on biquaternions." American Journal of Mathematics 7 (4): 293–326. JSTOR. 
Conway, Arthur W. 1911. "On the application of quaternions to some recent developments in electrical theory." Proceedings of the Royal Irish Academy 29A: 1–9.
Furey, C. 2012. "Unified Theory of Ideals." Physics Review D 86 (2): 025024. . Bibcode 2012PhRvD..86b5024F |s2cid=118458623.
Girard, P. R.1984. "The quaternion group and modern physics." European Journal of Physics 5 (1): 25–32. Bibcode 1984EJPh....5...25G. .
Hamilton, William Rowan. 1866. Elements of Quaternions. Ed. a Gulielmo Eduino Hamilton, filio patris mortui. University of Dublin Press.
Hamilton, William Rowan. 1899. Elements of Quaternions, vol. I, (1901). vol. II. Liber editus a Carolo Jasper Joly. Longmans, Green & Co.
Kilmister, C. W. 1994. Eddington's search for a fundamental theory. Cantabrigiae: Cambridge University Press. ISBN 978-0-521-37165-0.
Kravchenko, Vladislav. 2003. Applied Quaternionic Analysis. Heldermann Verlag. ISBN 3-88538-228-8.
Sangwine, Stephen J., Todd A. Ell, et Nicolas Le Bihan. 2010. "Fundamental representations and algebraic properties of biquaternions or complexified quaternions." Advances in Applied Clifford Algebras 21 (3): 1–30. . Arxiv 1001.0240.
Sangwine, Stephen J., et Daniel Alfsmann. 2010. "Determination of the biquaternion divisors of zero, including idempotents and nilpotents." Advances in Applied Clifford Algebras 20 (2): 401–410. Bibcode 2008arXiv0812.1102S. .
Silberstein, Ludwik. 1912. "Quaternionic form of relativity." Philosophical Magazine series 6: 23 (137): 790–809. . URL.
Silberstein, Ludwik. 1914. The Theory of Relativity.
Synge, J. L. 1972. "Quaternions, Lorentz transformations, and the Conway-Dirac-Eddington matrices." Communications of the Dublin Institute for Advanced Studies series A, vol. 21.
Tanişli, M. 2006. "Gauge transformation and electromagnetism with biquaternions." Europhysics Letters 74 (4): 569. Bibcode = 2006EL.....74..569T. .

Categoria:Algebra
Categoria:Gulielmus Rowan Hamilton
Categoria:Numeri
Categoria:Physica