Biquaternium

[thumb|upright=0.6|Gulielmus Rowan Hamilton [eques.]]
**Biquaternium** (Anglice *biquaternion*) in algebra abstracta est ullus ex numeris  w + x i + y j + z k, ubi w,\  x,\   y, et z sunt numeri complexi vel eorum variantes, et elementa 1,\   i,\   j,\   k 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. 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 \mathbb{C} \otimes \mathbb{H} (supra reales) ubi \mathbb{C} est campus numerorum complexorum et \mathbb{H} est algebra divisionis quaterniorum realium; quod breviter significat biquaternia esse complexificationem tantum quaterniorum. Biquaternia, cum genus algebrae complexae videantur,  isomorphica ad algebram 2 \times 2 matricum complexarum M_2(\mathbb{C}) sunt. Etiam sunt isomorphica ad nonnullas algebras Cliffordianas, inter quas 1=\mathbb{H}(\mathbb{C}) = C^0_3(\mathbb{C}) = C\ell_2(\mathbb{C}) = C\ell_{1,2}(\mathbb{R}), algebram Paulianam C\ell_{3,0}(\mathbb{R}), et par algebrae spatiotemporalis pars  C\ell^0_{1,3}(\mathbb{R}) = C\ell^0_{3,1}(\mathbb{\mathbb{R}}).

## 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