Classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center

Bin Ren; Lin Sheng Zhu

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 4, page 953-965
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Ren, Bin, and Zhu, Lin Sheng. "Classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center." Czechoslovak Mathematical Journal 67.4 (2017): 953-965. <http://eudml.org/doc/294583>.

@article{Ren2017,
abstract = {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.},
author = {Ren, Bin, Zhu, Lin Sheng},
journal = {Czechoslovak Mathematical Journal},
keywords = {related set; basis; derivation},
language = {eng},
number = {4},
pages = {953-965},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center},
url = {http://eudml.org/doc/294583},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Ren, Bin
AU - Zhu, Lin Sheng
TI - Classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 953
EP - 965
AB - 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.
LA - eng
KW - related set; basis; derivation
UR - http://eudml.org/doc/294583
ER -

References

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  1. Ancochea-Bermudez, J. M., Goze, M., 10.1007/BF01193621, Arch. Math. 50 (1988), 511-525 French. (1988) Zbl0628.17005MR0948265DOI10.1007/BF01193621
  2. Ancochea-Bermudez, J. M., Goze, M., 10.1007/BF01191272, Arch. Math. 52 (1989), 175-185 French. (1989) Zbl0672.17005MR0985602DOI10.1007/BF01191272
  3. Galitski, L. Y., Timashev, D. A., On classification of metabelian Lie algebras, J. Lie Theory 9 (1999), 125-156. (1999) Zbl0923.17015MR1680007
  4. Gauger, M. A., 10.2307/1996506, Trans. Am. Math. Soc. 179 (1973), 293-329. (1973) Zbl0267.17015MR0325719DOI10.2307/1996506
  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). (1998) MR2698220
  6. Goze, M., Khakimdjanov, Y., 10.1007/978-94-017-2432-6, Mathematics and Its Applications 361, Kluwer Academic Publishers, Dordrecht (1996). (1996) Zbl0845.17012MR1383588DOI10.1007/978-94-017-2432-6
  7. Goze, M., Remm, E., 10.1515/gmj-2015-0022, Georgian Math. J. 22 (2015), 219-234. (2015) Zbl06458841MR3353570DOI10.1515/gmj-2015-0022
  8. Khuhirun, B., Misra, K. C., Stitzinger, E., 10.1016/j.jalgebra.2015.07.036, J. Algebra 444 (2015), 328-338. (2015) Zbl1358.17013MR3406181DOI10.1016/j.jalgebra.2015.07.036
  9. Leger, G., Luks, E., 10.1017/s0027763000014525, Nagoya Math. J. 44 (1971), 39-50. (1971) Zbl0264.17003MR0297828DOI10.1017/s0027763000014525
  10. Remm, E., 10.1080/00927872.2016.1233238, Commun. Algebra 45 (2017), 2956-2966. (2017) MR3594570DOI10.1080/00927872.2016.1233238
  11. Ren, B., Meng, D. J., Some completable 2-step nilpotent Lie algebras I, Linear Algebra Appl. 338 (2001), 77-98. (2001) Zbl0992.17005MR1860314
  12. Ren, B., Zhou, L. S., 10.1080/00927872.2010.483342, Commun. Algebra 39 (2011), 2068-2081. (2011) Zbl1290.17004MR2813164DOI10.1080/00927872.2010.483342
  13. Revoy, P., 10.5802/afst.547, Ann. Fac. Sci. Toulouse, V. Ser., Math. 2 (1980), 93-100 French. (1980) Zbl0447.17007MR0595192DOI10.5802/afst.547
  14. Santharoubane, L. J., 10.4153/CJM-1982-084-5, Can. J. Math. 34 (1982), 1215-1239. (1982) Zbl0495.17011MR0678665DOI10.4153/CJM-1982-084-5
  15. Seeley, C., 10.2307/2154390, Trans. Am. Math. Soc. 335 (1993), 479-496. (1993) Zbl0770.17003MR1068933DOI10.2307/2154390
  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). (1891) 
  17. Yan, Z., Deng, S., 10.1007/s10587-013-0057-6, Czech. Math. J. 63 (2013), 847-863. (2013) Zbl1291.17013MR3125659DOI10.1007/s10587-013-0057-6

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