98
Views
8
CrossRef citations to date
0
Altmetric
Articles

Classification of nilpotent evolution algebras and extensions of their derivations

, &
Pages 4155-4169 | Received 12 Sep 2019, Accepted 15 Apr 2020, Published online: 28 Apr 2020

References

  • Barr, M., Knus, M.-A. (1971). Extensions of derivations. Proc. AMS 28(1):313–314. DOI: 10.2307/2037807.
  • Camacho, L. M., Gómez, J. R., Omirov, B. A., Turdibaev, R. M. (2013). The derivations of some evolution algebras. Linear Multilinear A. 61(3):309–322. DOI: 10.1080/03081087.2012.678342.
  • Camacho, L. M., Gómez, J. R., Omirov, B. A., Turdibaev, R. M. (2013). Some properties of evolution algebras. Bull. Korean Math. Soc. 50(5):1481–1494. DOI: 10.4134/BKMS.2013.50.5.1481.
  • Casado, C. Y., Molina, M. S., Velasco, M. V. (2017). Classification of three-dimensional evolution algebras. Linear Algebra Appl. 524(1):68–108. DOI: 10.1016/j.laa.2017.02.015.
  • Casas, J. M., Ladra, M., Omirov, B. A., Rozikov, U. A. (2013). On nilpotent index and dibaricity of evolution algebras. Linear Algebra Appl. 439(1):90–105. DOI: 10.1016/j.laa.2013.03.006.
  • Casas, J. M., Ladra, M., Omirov, B. A., Rozikov, U. A. (2014). On evolution algebras. Algebra Colloq. 21(02):331–342. DOI: 10.1142/S1005386714000285.
  • Costa, R. (1982). On the derivation algebra of gametic algebras for polyploidy with multiple alleles. Bol. Soc. Bras. Mat. 13(2):69–81. DOI: 10.1007/BF02584678.
  • Costa, R. (1983). On the derivation algebra of zygotic algebras for polyploidy with multiple alleles. Bol. Soc. Bras. Mat. 14(1):63–80. DOI: 10.1007/BF02584745.
  • Elduque, A., Labra, A. (2016). On nilpotent evolution algebras. Linear Algebra Appl. 505:11–31. DOI: 10.1016/j.laa.2016.04.025.
  • Ganikhodzhaev, R., Mukhamedov, F., Pirnapasov, A., Qaralleh, I. (2018). On genetic Volterra algebras and their derivations. Commun. Algebra 46(3):1353–1366. DOI: 10.1080/00927872.2017.1347663.
  • Gonshor, H. (1988). Derivations in genetic algebras. Commun. Algebra 16(8):1525–1542. DOI: 10.1080/00927879808823643.
  • Hegazi, A. S., Abdelwahab, H. (2015). Nilpotent evolution algebras over arbitrary fields. Linear Algebra Appl. 486:345–360. DOI: 10.1016/j.laa.2015.07.041.
  • Jacobson, N. (1955). Automorphisms and derivations of Lie algebras. Proc. Amer. Math. Soc. 6(2):281–283. DOI: 10.1090/S0002-9939-1955-0068532-9.
  • Khudoyberdiyev, A. K., Omirov, B. A., Qaralleh, I. (2015). Few remarks on evolution algebras. J. Algebra Appl. 14(04):1550053. DOI: 10.1142/S021949881550053X.
  • Labra, A., Ladra, M., Rozikov, U. A. (2014). An evolution algebra in population genetics. Linear Algebra Appl. 457:348–362. DOI: 10.1016/j.laa.2014.05.036.
  • Mukhamedov, F., Qaralleh, I. (2014). On derivations of genetic algebras. J. Phys: Conf. Ser. 553:012004. DOI: 10.1088/1742-6596/553/1/012004.
  • Mukhamedov, F., Qaralleh, I., Pirnapasov, A. (2016). On genetic and evolution algebras in dimension three. Int. J. Algebra 10(0 ): 327–334.
  • Tian, J. P. (2008). Evolution algebras and their applications. Lecture Notes in Mathematics, 1921, Berlin: Springer-Verlag.
  • Tian, J. P., Vojtechovsky, P. (2006). Mathematical concepts of evolution algebras in non-Mendelian genetics. Quasigroups Relat. Syst. 14(1):111–122.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.