| Title:
|
Classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center (English) |
| Author:
|
Ren, Bin |
| Author:
|
Zhu, Lin Sheng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
953-965 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A Lie algebra $L$ is called 2-step nilpotent if $L$ is not abelian and $[L, L]$ lies in the center of $L$. 2-step nilpotent Lie algebras are useful in the study of some geometric problems, and their classification has been an important problem in Lie theory. In this paper, we give a classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center. (English) |
| Keyword:
|
related set |
| Keyword:
|
basis |
| Keyword:
|
derivation |
| MSC:
|
17B05 |
| MSC:
|
17B30 |
| idZBL:
|
Zbl 06819565 |
| idMR:
|
MR3736011 |
| DOI:
|
10.21136/CMJ.2017.0253-16 |
| . |
| Date available:
|
2017-11-20T14:53:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146959 |
| . |
| Reference:
|
[1] Ancochea-Bermudez, J. M., Goze, M.: Classification des algèbres de Lie filiformes de dimension 8.Arch. Math. 50 (1988), 511-525 French. Zbl 0628.17005, MR 0948265, 10.1007/BF01193621 |
| Reference:
|
[2] Ancochea-Bermudez, J. M., Goze, M.: Classification des algèbres de Lie nilpotentes complexes de dimension 7.Arch. Math. 52 (1989), 175-185 French. Zbl 0672.17005, MR 0985602, 10.1007/BF01191272 |
| Reference:
|
[3] Galitski, L. Y., Timashev, D. A.: On classification of metabelian Lie algebras.J. Lie Theory 9 (1999), 125-156. Zbl 0923.17015, MR 1680007 |
| Reference:
|
[4] Gauger, M. A.: On the classification of metabelian Lie algebras.Trans. Am. Math. Soc. 179 (1973), 293-329. Zbl 0267.17015, MR 0325719, 10.2307/1996506 |
| Reference:
|
[5] Gong, M.-P.: Classification of Nilpotent Lie Algebras of Dimension 7 (over Algebraically Closed Fields and R).Ph.D. Thesis, University of Waterloo, Waterloo (1998). MR 2698220 |
| Reference:
|
[6] Goze, M., Khakimdjanov, Y.: Nilpotent Lie Algebras.Mathematics and Its Applications 361, Kluwer Academic Publishers, Dordrecht (1996). Zbl 0845.17012, MR 1383588, 10.1007/978-94-017-2432-6 |
| Reference:
|
[7] Goze, M., Remm, E.: $k$-step nilpotent Lie algebras.Georgian Math. J. 22 (2015), 219-234. Zbl 06458841, MR 3353570, 10.1515/gmj-2015-0022 |
| Reference:
|
[8] Khuhirun, B., Misra, K. C., Stitzinger, E.: On nilpotent Lie algebras of small breadth.J. Algebra 444 (2015), 328-338. Zbl 1358.17013, MR 3406181, 10.1016/j.jalgebra.2015.07.036 |
| Reference:
|
[9] Leger, G., Luks, E.: On derivations and holomorphs of nilpotent Lie algebras.Nagoya Math. J. 44 (1971), 39-50. Zbl 0264.17003, MR 0297828, 10.1017/s0027763000014525 |
| Reference:
|
[10] Remm, E.: Breadth and characteristic sequence of nilpotent Lie algebras.Commun. Algebra 45 (2017), 2956-2966. MR 3594570, 10.1080/00927872.2016.1233238 |
| Reference:
|
[11] Ren, B., Meng, D. J.: Some completable 2-step nilpotent Lie algebras I.Linear Algebra Appl. 338 (2001), 77-98. Zbl 0992.17005, MR 1860314 |
| Reference:
|
[12] Ren, B., Zhou, L. S.: Classification of 2-step nilpotent Lie algebras of dimension 8 with 2-dimensional center.Commun. Algebra 39 (2011), 2068-2081. Zbl 1290.17004, MR 2813164, 10.1080/00927872.2010.483342 |
| Reference:
|
[13] Revoy, P.: Algèbres de Lie métabéliennes.Ann. Fac. Sci. Toulouse, V. Ser., Math. 2 (1980), 93-100 French. Zbl 0447.17007, MR 0595192, 10.5802/afst.547 |
| Reference:
|
[14] Santharoubane, L. J.: Kac-Moody Lie algebras and the classification of nilpotent Lie algebras of maximal rank.Can. J. Math. 34 (1982), 1215-1239. Zbl 0495.17011, MR 0678665, 10.4153/CJM-1982-084-5 |
| Reference:
|
[15] Seeley, C.: 7-dimensional nilpotent Lie algebras.Trans. Am. Math. Soc. 335 (1993), 479-496. Zbl 0770.17003, MR 1068933, 10.2307/2154390 |
| Reference:
|
[16] Umlauf, K. A.: Über die Zusammensetzung der endlichen continuierlichen Transformationsgruppen insbesondere der Gruppen vom Range Null.Ph.D. Thesis, University of Leipzig, Leipzig German (1891). |
| Reference:
|
[17] Yan, Z., Deng, S.: The classification of two step nilpotent complex Lie algebras of dimension 8.Czech. Math. J. 63 (2013), 847-863. Zbl 1291.17013, MR 3125659, 10.1007/s10587-013-0057-6 |
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