Unified computational approach to nilpotent algebra classification problems

Shirali Kadyrov; Farukh Mashurov

Communications in Mathematics (2021)

  • Volume: 29, Issue: 2, page 215-226
  • ISSN: 1804-1388

Abstract

top
In this article, we provide an algorithm with Wolfram Mathematica code that gives a unified computational power in classification of finite dimensional nilpotent algebras using Skjelbred-Sund method. To illustrate the code, we obtain new finite dimensional Moufang algebras.

How to cite

top

Kadyrov, Shirali, and Mashurov, Farukh. "Unified computational approach to nilpotent algebra classification problems." Communications in Mathematics 29.2 (2021): 215-226. <http://eudml.org/doc/297680>.

@article{Kadyrov2021,
abstract = {In this article, we provide an algorithm with Wolfram Mathematica code that gives a unified computational power in classification of finite dimensional nilpotent algebras using Skjelbred-Sund method. To illustrate the code, we obtain new finite dimensional Moufang algebras.},
author = {Kadyrov, Shirali, Mashurov, Farukh},
journal = {Communications in Mathematics},
keywords = {Algebra; Skjelbred-Sund classification; finite dimensional nilpotent algebra; Wolfram Mathematica; symbolic solver; algorithm},
language = {eng},
number = {2},
pages = {215-226},
publisher = {University of Ostrava},
title = {Unified computational approach to nilpotent algebra classification problems},
url = {http://eudml.org/doc/297680},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Kadyrov, Shirali
AU - Mashurov, Farukh
TI - Unified computational approach to nilpotent algebra classification problems
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 2
SP - 215
EP - 226
AB - In this article, we provide an algorithm with Wolfram Mathematica code that gives a unified computational power in classification of finite dimensional nilpotent algebras using Skjelbred-Sund method. To illustrate the code, we obtain new finite dimensional Moufang algebras.
LA - eng
KW - Algebra; Skjelbred-Sund classification; finite dimensional nilpotent algebra; Wolfram Mathematica; symbolic solver; algorithm
UR - http://eudml.org/doc/297680
ER -

References

top
  1. Abdelwahab, H., Calderón, A.J., Kaygorodov, I., 10.1142/S0218196719500437, International Journal of Algebra and Computation, 29, 6, 2019, 1113-1129, (2019) MR3996987DOI10.1142/S0218196719500437
  2. Camacho, L., Kaygorodov, I., Lopatkin, V., Salim, M., 10.2478/cm-2020-0019, Communications in Mathematics, 28, 2, 2020, 161-178, (2020) DOI10.2478/cm-2020-0019
  3. Cicalò, S., Graaf, W. De, Schneider, C., 10.1016/j.laa.2011.06.037, Linear Algebra and its Applications, 436, 1, 2012, 163-189, (2012) DOI10.1016/j.laa.2011.06.037
  4. Calderón, A.J., Ouaridi, A.F., Kaygorodov, I., 10.1080/03081087.2020.1849001, Linear and Multilinear Algebra, 2020, 1-24, DOI: 10.1080/03081087.2020.1849001. (2020) DOI10.1080/03081087.2020.1849001
  5. Jumaniyozov, D., Kaygorodov, I., Khudoyberdiyev, A., 10.1142/S0219498821502029, Journal of Algebra and its Applications, 2020, DOI: 10.1142/S0219498821502029. (2020) DOI10.1142/S0219498821502029
  6. Graaf, W. De, 10.1142/S0218196718500078, International Journal of Algebra and Computation, 28, 1, 2018, 133-161, (2018) DOI10.1142/S0218196718500078
  7. Gorshkov, I., Kaygorodov, I., Khrypchenko, M., The algebraic classification of nilpotent Tortkara algebras, Communications in Algebra, 48, 8, 2020, 3608-3623, (2020) 
  8. Gorshkov, I., Kaygorodov, I., Kytmanov, A., Salim, M., 10.17516/1997-1397-2019-12-2-173-184, Journal of Siberian Federal University. Mathematics & Physics, 12, 2, 2019, 173-184, (2019) DOI10.17516/1997-1397-2019-12-2-173-184
  9. Goze, M., Remm, E., 2-dimensional algebras, African Journal Of Mathematical Physics, 10, 2, 2011, 81-91, (2011) 
  10. Hegazi, A.S., Abdelwahab, H., 10.1016/j.laa.2016.01.015, Linear Algebra and its Applications, 494, 2016, 165-218, (2016) DOI10.1016/j.laa.2016.01.015
  11. Hegazi, A.S., Abdelwahab, H., 10.1080/00927872.2017.1327052, Communications in Algebra, 46, 2, 2018, 629-643, (2018) DOI10.1080/00927872.2017.1327052
  12. Hegazi, A.S., Abdelwahab, H., Martin, A.J. Calderón, 10.1016/j.laa.2016.04.029, Linear Algebra and its Applications, 505, 2016, 32-56, (2016) DOI10.1016/j.laa.2016.04.029
  13. Ismailov, N., Kaygorodov, I., Mashurov, F., 10.1007/s10468-019-09935-y, Algebras and Representation Theory, 24, 2021, 135-148, (2021) DOI10.1007/s10468-019-09935-y
  14. Kadyrov, S., Mashurov, F., Nilpotent algebra classifier code, 2020, https://www.wolframcloud.com/obj/39e8169f-8fbf-4540-aa65-4b01f187f63f. (2020) 
  15. Karimjanov, I., Kaygorodov, I., Khudoyberdiyev, A., 10.1016/j.geomphys.2019.04.016, Journal of Geometry and Physics, 143, 2019, 11-21, (2019) DOI10.1016/j.geomphys.2019.04.016
  16. Kaygorodov, I., Páez-Guillán, M.P., Voronin, V., The algebraic and geometric classification of nilpotent bicommutative algebras, Algebras and Representation Theory , 23, 2020, 2331-2347, (2020) 
  17. Kaygorodov, I., Volkov, Yu., 10.4153/S0008414X18000056, Canadian Journal of Mathematics , 71, 4, 2019, 819-842, (2019) DOI10.4153/S0008414X18000056
  18. Loginov, E. K., 10.1007/BF01209084, Mathematical Notes , 54, 6, 1993, 1230-1235, (1993) DOI10.1007/BF01209084
  19. Mashurov, F., Kaygorodov, I., 10.1142/S0219498822500311, Journal of Algebra and Its Applications, 2020, DOI: 10.1142/S0219498822500311. (2020) DOI10.1142/S0219498822500311
  20. Shestakov, I., Pérez-Izquierdo, J.M., 10.1016/S0021-8693(03)00389-2, Journal of Algebra, 272, 1, 2004, 379-393, (2004) DOI10.1016/S0021-8693(03)00389-2
  21. Skjelbred, T., Sund, T., On the classification of nilpotent Lie algebras, Preprint series. Pure Mathematics, 1977, http://urn.nb.no/URN:NBN:no-48289. (1977) 
  22. Zinbiel, G.W., Encyclopedia of types of algebras 2010, Proceedings of the International Conference in Nankai Series in Pure Applied Mathematics and Theoretical Physics, 9, 2012, 217298, (2012) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.