대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제50권5호
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  • Pages.1481-1494
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  • 2013
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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SOME PROPERTIES OF EVOLUTION ALGEBRAS

  • Camacho, L.M. (Dpto. Matematica Aplicada I Universidad de Sevilla) ;
  • Gomez, J.R. (Universidad de Sevilla) ;
  • Omirov, B.A. (Institute of Mathematics and Information Technologies) ;
  • Turdibaev, R.M. (Department of Mathematics National University of Uzbekistan)
  • 투고 : 2011.10.07
  • 발행 : 2013.09.30
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초록

The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras the criterium of nilpotency is established in terms of the properties of corresponding matrices. Moreover, it is proved that for nilpotent $n$-dimensional complex evolution algebras the possible maximal nilpotency index is $1+2^{n-1}$.

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참고문헌

  1. J. M. Casas, M. Ladra, B. A. Omirov, and U. A. Rozikov, On evolution algebras, Algebra Colloquium. arXiv:1004.1050v1 (to appear).
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피인용 문헌

  1. Evolution algebras of arbitrary dimension and their decompositions vol.495, 2016, https://doi.org/10.1016/j.laa.2016.01.007
  2. Few remarks on evolution algebras vol.14, pp.04, 2015, https://doi.org/10.1142/S021949881550053X
  3. Algebraic computation of genetic patterns related to three-dimensional evolution algebras 2017, https://doi.org/10.1016/j.amc.2017.05.045
  4. Nilpotent evolution algebras over arbitrary fields vol.486, 2015, https://doi.org/10.1016/j.laa.2015.07.041
  5. Evolution algebras and graphs vol.14, pp.07, 2015, https://doi.org/10.1142/S0219498815501030
  6. Classification of asexual diploid organisms by means of strongly isotopic evolution algebras defined over any field vol.472, 2017, https://doi.org/10.1016/j.jalgebra.2016.11.018
  7. On Evolution Algebras vol.21, pp.02, 2014, https://doi.org/10.1142/S1005386714000285
  8. On real chains of evolution algebras vol.63, pp.3, 2015, https://doi.org/10.1080/03081087.2014.889131
  9. On the Property of Subalgebras of Evolution Algebras pp.1572-9079, 2018, https://doi.org/10.1007/s10468-018-9767-7
  10. Characterization theorems for the spaces of derivations of evolution algebras associated to graphs pp.1563-5139, 2018, https://doi.org/10.1080/03081087.2018.1541962
  11. Evolution coalgebras pp.1563-5139, 2018, https://doi.org/10.1080/03081087.2018.1460795
  12. The connection between evolution algebras, random walks and graphs pp.1793-6829, 2020, https://doi.org/10.1142/S0219498820500231
  13. A class of nilpotent evolution algebras pp.1532-4125, 2019, https://doi.org/10.1080/00927872.2018.1508584