The variety of dual mock-Lie algebras

Luisa M. Camacho; Ivan Kaygorodov; Viktor Lopatkin; Mohamed A. Salim

Communications in Mathematics (2020)

  • Volume: 28, Issue: 2, page 161-178
  • ISSN: 1804-1388

Abstract

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We classify all complex 7 - and 8 -dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex 9 -dimensional dual mock-Lie algebras.

How to cite

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Camacho, Luisa M., et al. "The variety of dual mock-Lie algebras." Communications in Mathematics 28.2 (2020): 161-178. <http://eudml.org/doc/297083>.

@article{Camacho2020,
abstract = {We classify all complex $7$- and $8$-dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex $9$-dimensional dual mock-Lie algebras.},
author = {Camacho, Luisa M., Kaygorodov, Ivan, Lopatkin, Viktor, Salim, Mohamed A.},
journal = {Communications in Mathematics},
keywords = {Nilpotent algebra; mock-Lie algebra; dual mock-Lie algebra; anticommutative algebra; algebraic classification; geometric classification; central extension; degeneration},
language = {eng},
number = {2},
pages = {161-178},
publisher = {University of Ostrava},
title = {The variety of dual mock-Lie algebras},
url = {http://eudml.org/doc/297083},
volume = {28},
year = {2020},
}

TY - JOUR
AU - Camacho, Luisa M.
AU - Kaygorodov, Ivan
AU - Lopatkin, Viktor
AU - Salim, Mohamed A.
TI - The variety of dual mock-Lie algebras
JO - Communications in Mathematics
PY - 2020
PB - University of Ostrava
VL - 28
IS - 2
SP - 161
EP - 178
AB - We classify all complex $7$- and $8$-dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex $9$-dimensional dual mock-Lie algebras.
LA - eng
KW - Nilpotent algebra; mock-Lie algebra; dual mock-Lie algebra; anticommutative algebra; algebraic classification; geometric classification; central extension; degeneration
UR - http://eudml.org/doc/297083
ER -

References

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  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. Alvarez, M.A., 10.1142/S100538671800024X, Algebra Colloquium, 25, 02, 2018, 349-360, (2018) MR3805328DOI10.1142/S100538671800024X
  3. Alvarez, M.A., The variety of 7 -dimensional 2 -step nilpotent Lie algebras, Symmetry, 10, 1, 2018, 26, Multidisciplinary Digital Publishing Institute, (2018) 
  4. Burde, D., Fialowski, A., Jacobi--Jordan algebras, Linear Algebra and its Applications, 459, 2014, 586-594, Elsevier, (2014) MR3247244
  5. Burde, D., Steinhoff, C., 10.1006/jabr.1998.7714, Journal of Algebra, 214, 2, 1999, 729-739, Academic Press, (1999) MR1680532DOI10.1006/jabr.1998.7714
  6. Cicalò , S., Graaf, W. De, Schneider, C., 10.1016/j.laa.2011.06.037, Linear Algebra and its Applications, 436, 1, 2012, 163-189, Elsevier, (2012) MR2859920DOI10.1016/j.laa.2011.06.037
  7. Darijani, I., Usefi, H., 10.1016/j.jalgebra.2016.06.011, Journal of Algebra, 464, 2016, 97-140, Elsevier, (2016) MR3533425DOI10.1016/j.jalgebra.2016.06.011
  8. Graaf, W.A. De, 10.1016/j.jalgebra.2006.08.006, Journal of Algebra, 309, 2, 2007, 640-653, Elsevier, (2007) MR2303198DOI10.1016/j.jalgebra.2006.08.006
  9. Graaf, W.A. De, Classification of nilpotent associative algebras of small dimension, International Journal of Algebra and Computation, 28, 01, 2018, 133-161, World Scientific, (2018) MR3768261
  10. Ouaridi, A. Fernandez, Kaygorodov, I., Khrypchenko, M., Yu. Volkov, Degenerations of nilpotent algebras, arXiv:1905.05361. 
  11. Gorshkov, I., Kaygorodov, I., Khrypchenko, M., 10.1080/00927872.2019.1635612, Communications in Algebra, 48, 1, 2020, 204-209, Taylor & Francis, (2020) MR4060024DOI10.1080/00927872.2019.1635612
  12. Grunewald, F., O'Halloran, J., 10.1016/0021-8693(88)90093-2, Journal of Algebra, 112, 2, 1988, 315-325, Academic Press, (1988) MR0926608DOI10.1016/0021-8693(88)90093-2
  13. Grunewald, F., O'Halloran, J., 10.1016/0021-8693(88)90199-8, Journal of Algebra, 116, 1, 1988, 163-175, Elsevier, (1988) MR0944153DOI10.1016/0021-8693(88)90199-8
  14. Hegazi, A.S., Abdelwahab, H., 10.1016/j.laa.2016.01.015, Linear Algebra and its Applications, 494, 2016, 165-218, Elsevier, (2016) MR3455692DOI10.1016/j.laa.2016.01.015
  15. Hegazi, A.S., Abdelwahab, H., Martin, A.J. Calderon, 10.1016/j.laa.2016.04.029, Linear Algebra and its Applications, 505, 2016, 32-56, Elsevier, (2016) MR3506483DOI10.1016/j.laa.2016.04.029
  16. Ismailov, N., Kaygorodov, I., Mashurov, F., 10.1007/s10468-019-09935-y, Algebras and Representation Theory, 2020, 14 pp, Springer, DOI: 10.1007/s10468-019-09935-y. (2020) MR4207393DOI10.1007/s10468-019-09935-y
  17. Ismailov, N., Kaygorodov, I., Yu. Volkov, 10.1142/S0129167X18500350, International Journal of Mathematics, 29, 05, 2018, Article 1850035, World Scientific, (2018) MR3808051DOI10.1142/S0129167X18500350
  18. Ismailov, N., Kaygorodov, I., Yu. Volkov, 10.4153/S0008439519000018, Canadian Mathematical Bulletin, 62, 3, 2019, 539-549, Canadian Mathematical Society, (2019) MR3998738DOI10.4153/S0008439519000018
  19. Karimjanov, I., Kaygorodov, I., Khudoyberdiyev, A., 10.1016/j.geomphys.2019.04.016, Journal of Geometry and Physics, 143, 2019, 11-21, Elsevier, (2019) MR3954151DOI10.1016/j.geomphys.2019.04.016
  20. Kaygorodov, I., Khrypchenko, M., Lopes, S., The algebraic and geometric classification of nilpotent anticommutative algebras, Journal of Pure and Applied Algebra, 224, 8, 2020, Article 106337, (2020) MR4074577
  21. Kaygorodov, I., Yu. Popov, Yu. Volkov, 10.1080/00927872.2018.1459647, Communications in Algebra, 46, 11, 2018, 4928-4940, Taylor & Francis, (2018) MR3864274DOI10.1080/00927872.2018.1459647
  22. Kaygorodov, I., Yu. Volkov, 10.4153/S0008414X18000056, Canadian Journal of Mathematics, 71, 4, 2019, 819-842, Canadian Mathematical Society, (2019) MR3984022DOI10.4153/S0008414X18000056
  23. Kaygorodov, I., Yu. Volkov, 10.17323/1609-4514-2019-19-3-485-521, Moscow Mathematical Journal, 19, 3, 2019, 485-521, (2019) MR3993005DOI10.17323/1609-4514-2019-19-3-485-521
  24. Okubo, S., Kamiya, N., 10.1006/jabr.1997.7144, Journal of Algebra, 198, 2, 1997, 388-411, Elsevier, (1997) MR1489904DOI10.1006/jabr.1997.7144
  25. Ren, B., Zhu, L.S., 10.21136/CMJ.2017.0253-16, Czechoslovak Mathematical Journal, 67, 4, 2017, 953-965, Springer, (2017) MR3736011DOI10.21136/CMJ.2017.0253-16
  26. Seeley, C., 10.1080/00927879008824088, Communications in Algebra, 18, 10, 1990, 3493-3505, Taylor & Francis, (1990) MR1063991DOI10.1080/00927879008824088
  27. Skjelbred, T., Sund, T., Sur la classification des algèbres de Lie nilpotentes, Comptes rendus de l'Académie des Sciences, 286, 5, 1978, A241-A242, (1978) MR0498734
  28. Zhevlakov, K.A., Solvability and nilpotency of Jordan rings, Algebra i Logika, 5, 3, 1966, 37-58, (1966) MR0207786
  29. Zusmanovich, P., 10.1090/S0002-9947-1992-1069751-2, Transactions of the American Mathematical Society, 334, 1, 1992, 143-152, (1992) MR1069751DOI10.1090/S0002-9947-1992-1069751-2
  30. Zusmanovich, P., 10.1016/j.laa.2016.12.029, Linear Algebra and its Applications, 518, 2017, 79-96, Elsevier, (2017) MR3598575DOI10.1016/j.laa.2016.12.029

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