Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras

Dev Karan Singh; Mani Shankar Pandey; Shiv Datt Kumar

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 1, page 283-299
  • ISSN: 0011-4642

Abstract

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This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras. The paper presents an innovative adaptation of the Hirsch-Plotkin theorem specifically tailored for multiplicative Lie algebras.

How to cite

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Singh, Dev Karan, Pandey, Mani Shankar, and Kumar, Shiv Datt. "Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras." Czechoslovak Mathematical Journal 74.1 (2024): 283-299. <http://eudml.org/doc/299247>.

@article{Singh2024,
abstract = {This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras. The paper presents an innovative adaptation of the Hirsch-Plotkin theorem specifically tailored for multiplicative Lie algebras.},
author = {Singh, Dev Karan, Pandey, Mani Shankar, Kumar, Shiv Datt},
journal = {Czechoslovak Mathematical Journal},
keywords = {multiplicative Lie algebra; commutator; nilpotent group; perfect group; central extensions},
language = {eng},
number = {1},
pages = {283-299},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras},
url = {http://eudml.org/doc/299247},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Singh, Dev Karan
AU - Pandey, Mani Shankar
AU - Kumar, Shiv Datt
TI - Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 1
SP - 283
EP - 299
AB - This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras. The paper presents an innovative adaptation of the Hirsch-Plotkin theorem specifically tailored for multiplicative Lie algebras.
LA - eng
KW - multiplicative Lie algebra; commutator; nilpotent group; perfect group; central extensions
UR - http://eudml.org/doc/299247
ER -

References

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  1. Bak, A., Donadze, G., Inassaridze, N., Ladra, M., 10.1016/j.jpaa.2006.03.029, J. Pure Appl. Algebra 208 (2007), 761-777. (2007) Zbl1138.18007MR2277710DOI10.1016/j.jpaa.2006.03.029
  2. Donadze, G., Inassaridze, N., Ladra, M., Vieites, A. M., 10.1016/j.jpaa.2017.08.006, J. Pure Appl. Algebra 222 (2018), 1786-1802. (2018) Zbl1408.18031MR3763283DOI10.1016/j.jpaa.2017.08.006
  3. Donadze, G., Ladra, M., More on five commutator identities, J. Homotopy Relat. Struct. 2 (2007), 45-55. (2007) Zbl1184.20033MR2326932
  4. Ellis, G. J., 10.1017/S1446788700036934, J. Aust. Math. Soc., Ser. A 54 (1993), 1-19. (1993) Zbl0777.20001MR1195654DOI10.1017/S1446788700036934
  5. Lal, R., 10.1007/978-981-10-4256-0, Infosys Science Foundation Series. Springer, Singapore (2017). (2017) Zbl1369.00003MR3642661DOI10.1007/978-981-10-4256-0
  6. Lal, R., Upadhyay, S. K., 10.1016/j.jpaa.2018.12.003, J. Pure Appl. Algebra 223 (2019), 3695-3721. (2019) Zbl1473.17050MR3944451DOI10.1016/j.jpaa.2018.12.003
  7. Pandey, M. S., Lal, R., Upadhyay, S. K., 10.1142/S0219498821501383, J. Algebra Appl. 20 (2021), Article ID 2150138, 11 pages. (2021) Zbl07411748MR4297322DOI10.1142/S0219498821501383
  8. Pandey, M. S., Upadhyay, S. K., Theory of extensions of multiplicative Lie algebras, J. Lie Theory 31 (2021), 637-658. (2021) Zbl1486.17033MR4257164
  9. Pandey, M. S., Upadhyay, S. K., 10.4064/cm8397-12-2020, Colloq. Math. 168 (2022), 25-34. (2022) Zbl1514.17025MR4378560DOI10.4064/cm8397-12-2020
  10. Point, F., Wantiez, P., 10.1016/0022-4049(95)00115-8, J. Pure Appl. Algebra 111 (1996), 229-243. (1996) Zbl0863.20015MR1394354DOI10.1016/0022-4049(95)00115-8
  11. Robinson, D. J. S., 10.1007/978-1-4419-8594-1, Graduate Texts in Mathematics 80. Springer, New York (1996). (1996) Zbl0836.20001MR1357169DOI10.1007/978-1-4419-8594-1
  12. Walls, G. L., 10.3906/mat-1904-55, Turk. J. Math. 43 (2019), 2888-2897. (2019) Zbl1429.20028MR4038386DOI10.3906/mat-1904-55

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