The structure and representation of n-ary algebras of DNA recombination

Sergei Sverchkov

Open Mathematics (2011)

  • Volume: 9, Issue: 6, page 1193-1216
  • ISSN: 2391-5455

Abstract

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In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. It is proved that every identity satisfied by n-ary DNA recombination, with no restriction on the degree, is a consequence of n-ary commutativity and a single n-ary identity of the degree 3n-2. It solves the well-known open problem in the theory of n-ary intermolecular recombination.

How to cite

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Sergei Sverchkov. "The structure and representation of n-ary algebras of DNA recombination." Open Mathematics 9.6 (2011): 1193-1216. <http://eudml.org/doc/269346>.

@article{SergeiSverchkov2011,
abstract = {In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. It is proved that every identity satisfied by n-ary DNA recombination, with no restriction on the degree, is a consequence of n-ary commutativity and a single n-ary identity of the degree 3n-2. It solves the well-known open problem in the theory of n-ary intermolecular recombination.},
author = {Sergei Sverchkov},
journal = {Open Mathematics},
keywords = {Jordan algebras; Formalization of DNA recombination; Splicing algebras; Special algebras; DNA recombination; splicing algebras; special algebras},
language = {eng},
number = {6},
pages = {1193-1216},
title = {The structure and representation of n-ary algebras of DNA recombination},
url = {http://eudml.org/doc/269346},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Sergei Sverchkov
TI - The structure and representation of n-ary algebras of DNA recombination
JO - Open Mathematics
PY - 2011
VL - 9
IS - 6
SP - 1193
EP - 1216
AB - In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. It is proved that every identity satisfied by n-ary DNA recombination, with no restriction on the degree, is a consequence of n-ary commutativity and a single n-ary identity of the degree 3n-2. It solves the well-known open problem in the theory of n-ary intermolecular recombination.
LA - eng
KW - Jordan algebras; Formalization of DNA recombination; Splicing algebras; Special algebras; DNA recombination; splicing algebras; special algebras
UR - http://eudml.org/doc/269346
ER -

References

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  1. [1] Bremner M.R., Jordan algebras arising from intermolecular recombination, SIGSAM Bull., 2005, 39(4), 106–117 http://dx.doi.org/10.1145/1140378.1140380 Zbl1226.17026
  2. [2] Bremner M.R., Polynomial identities for ternary intermolecular recombination, Discrete Contin. Dyn. Syst. Ser. S, 2011, 4(6), 1387–1399 http://dx.doi.org/10.3934/dcdss.2011.4.1387 Zbl1256.17001
  3. [3] Cohn P.M., On homomorphic images of special Jordan algebras, Canad. J. Math., 1954, 6, 253–264 http://dx.doi.org/10.4153/CJM-1954-026-9 Zbl0055.02704
  4. [4] Einstein A., Podolsky B., Rosen N., Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev., 1935, 47(10), 777–780 http://dx.doi.org/10.1103/PhysRev.47.777 Zbl0012.04201
  5. [5] Jacobson N., Lie Algebras, Interscience Tracts in Pure and Applied Mathematics, 10, Interscience, New York-London, 1962 Zbl0121.27504
  6. [6] Jordan P., Über Verallgemeinerungsmöglichkeiten des Formalismus der Quantenmechanik, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. I, 1933, 41, 209–217 Zbl0007.08502
  7. [7] Landweber L.F., Kari L., The evolution on cellular computing: natire’s solution to a computational problem, BioSystems, 1999, 52(1–3), 3–13 http://dx.doi.org/10.1016/S0303-2647(99)00027-1 
  8. [8] Mal’cev A.I., Algebraic Systems, Grundlehren Math. Wiss., 192, Springer, Berlin-Heidelberg-New York, 1973 
  9. [9] Morgan T.H., A Critique of the Theory of Evolution, Princeton University Press, Princeton, 1916 
  10. [10] Robbins D.P., Jordan elements in a free associative algebra. I, J. Algebra, 1971, 19(3), 354–378 http://dx.doi.org/10.1016/0021-8693(71)90095-0 
  11. [11] Slin’ko A.M., On special varieties of Jordan algebras, Mat. Zametki, 1979, 26(3), 337–344 (in Russian) 
  12. [12] Sverchkov S., Varieties of special algebras, Comm. Algebra, 1988, 16(9), 1877–1919 http://dx.doi.org/10.1080/00927878808823665 Zbl0661.17028
  13. [13] Sverchkov S.R., Structure and representation of Jordan algebras arising from intermolecular recombination, In: Algebras, Representations and Applications, Maresias, August 26–September 1, 2007, Contemp. Math. 483, American Mathematical Society, Providence, 2009, 261–285 Zbl1196.17024
  14. [14] Zhevlakov K.A., Slin’ko A.M., Shestakov I.P., Shirshov A.I., Rings that are Nearly Associative, Pure Appl. Math., 104, Academic Press, New York-London, 1982 

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