| Title:
|
Unified computational approach to nilpotent algebra classification problems (English) |
| Author:
|
Kadyrov, Shirali |
| Author:
|
Mashurov, Farukh |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
215-226 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Algebra |
| Keyword:
|
Skjelbred-Sund classification |
| Keyword:
|
finite dimensional nilpotent algebra |
| Keyword:
|
Wolfram Mathematica |
| Keyword:
|
symbolic solver |
| Keyword:
|
algorithm |
| MSC:
|
17A30 |
| MSC:
|
68W30 |
| idZBL:
|
Zbl 07426419 |
| idMR:
|
MR4285752 |
| . |
| Date available:
|
2021-11-04T12:14:41Z |
| Last updated:
|
2021-12-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149190 |
| . |
| Reference:
|
[1] Abdelwahab, H., Calderón, A.J., Kaygorodov, I.: The algebraic and geometric classification of nilpotent binary Lie algebras.International Journal of Algebra and Computation, 29, 6, 2019, 1113-1129, MR 3996987, 10.1142/S0218196719500437 |
| Reference:
|
[2] Camacho, L., Kaygorodov, I., Lopatkin, V., Salim, M.: The variety of dual Mock-Lie algebras.Communications in Mathematics, 28, 2, 2020, 161-178, 10.2478/cm-2020-0019 |
| Reference:
|
[3] Cicalò, S., Graaf, W. De, Schneider, C.: Six-dimensional nilpotent Lie algebras.Linear Algebra and its Applications, 436, 1, 2012, 163-189, 10.1016/j.laa.2011.06.037 |
| Reference:
|
[4] Calderón, A.J., Ouaridi, A.F., Kaygorodov, I.: On the classification of bilinear maps with radical of a fixed codimension.Linear and Multilinear Algebra, 2020, 1-24, DOI: 10.1080/03081087.2020.1849001. 10.1080/03081087.2020.1849001 |
| Reference:
|
[5] Jumaniyozov, D., Kaygorodov, I., Khudoyberdiyev, A.: The algebraic and geometric classification of nilpotent noncommutative Jordan algebras.Journal of Algebra and its Applications, 2020, DOI: 10.1142/S0219498821502029. 10.1142/S0219498821502029 |
| Reference:
|
[6] Graaf, W. De: Classification of nilpotent associative algebras of small dimension.International Journal of Algebra and Computation, 28, 1, 2018, 133-161, 10.1142/S0218196718500078 |
| Reference:
|
[7] Gorshkov, I., Kaygorodov, I., Khrypchenko, M.: The algebraic classification of nilpotent Tortkara algebras.Communications in Algebra, 48, 8, 2020, 3608-3623, |
| Reference:
|
[8] Gorshkov, I., Kaygorodov, I., Kytmanov, A., Salim, M.: The variety of nilpotent Tortkara algebras. Journal of Siberian Federal University. Mathematics & Physics, 12, 2, 2019, 173-184, 10.17516/1997-1397-2019-12-2-173-184 |
| Reference:
|
[9] Goze, M., Remm, E.: 2-dimensional algebras.African Journal Of Mathematical Physics, 10, 2, 2011, 81-91, |
| Reference:
|
[10] Hegazi, A.S., Abdelwahab, H.: Classification of five-dimensional nilpotent Jordan algebras.Linear Algebra and its Applications, 494, 2016, 165-218, 10.1016/j.laa.2016.01.015 |
| Reference:
|
[11] Hegazi, A.S., Abdelwahab, H.: The classification of n-dimensional non-associative Jordan algebras with $(n-3)$-dimensional annihilator.Communications in Algebra, 46, 2, 2018, 629-643, 10.1080/00927872.2017.1327052 |
| Reference:
|
[12] Hegazi, A.S., Abdelwahab, H., Martin, A.J. Calderón: The classification of n-dimensional non-Lie Malcev algebras with $(n-4)$-dimensional annihilator.Linear Algebra and its Applications, 505, 2016, 32-56, 10.1016/j.laa.2016.04.029 |
| Reference:
|
[13] Ismailov, N., Kaygorodov, I., Mashurov, F.: The Algebraic and Geometric Classification of Nilpotent Assosymmetric Algebras.Algebras and Representation Theory, 24, 2021, 135-148, 10.1007/s10468-019-09935-y |
| Reference:
|
[14] Kadyrov, S., Mashurov, F.: Nilpotent algebra classifier code.2020, https://www.wolframcloud.com/obj/39e8169f-8fbf-4540-aa65-4b01f187f63f. |
| Reference:
|
[15] Karimjanov, I., Kaygorodov, I., Khudoyberdiyev, A.: The algebraic and geometric classification of nilpotent Novikov algebras.Journal of Geometry and Physics, 143, 2019, 11-21, 10.1016/j.geomphys.2019.04.016 |
| Reference:
|
[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, |
| Reference:
|
[17] Kaygorodov, I., Volkov, Yu.: The variety of 2-dimensional algebras over an algebraically closed field.Canadian Journal of Mathematics , 71, 4, 2019, 819-842, 10.4153/S0008414X18000056 |
| Reference:
|
[18] Loginov, E. K.: Embedding of Strongly Simple Moufang Loops In Simple Alternative Algebras.Mathematical Notes , 54, 6, 1993, 1230-1235, 10.1007/BF01209084 |
| Reference:
|
[19] Mashurov, F., Kaygorodov, I.: One-generated nilpotent assosymmetric algebras.Journal of Algebra and Its Applications, 2020, DOI: 10.1142/S0219498822500311. 10.1142/S0219498822500311 |
| Reference:
|
[20] Shestakov, I., Pérez-Izquierdo, J.M.: An envelope for Malcev algebras.Journal of Algebra, 272, 1, 2004, 379-393, 10.1016/S0021-8693(03)00389-2 |
| Reference:
|
[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. |
| Reference:
|
[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, |
| . |
