Home Multiplicative Lie algebra structure on a nilpotent group of class 2
Article
Licensed
Unlicensed Requires Authentication

Multiplicative Lie algebra structure on a nilpotent group of class 2

  • Deepak Pal , Amit Kumar and Sumit Kumar Upadhyay EMAIL logo
Published/Copyright: July 9, 2025
Become an author with De Gruyter Brill

Abstract

This paper explores the properties of multiplicative Lie algebra structures on a nilpotent group of class 2.

MSC 2020: 20F14; 20F18; 20K35

Funding statement: The first named author sincerely thanks IIIT Allahabad and Ministry of Education, Government of India for providing institute fellowship. The second named author sincerely thanks IIIT Allahabad and University grant commission (UGC), Govt. of India, New Delhi for research fellowship. The third named author is thankful to National Board for Higher Mathematics (NBHM), Government of India for the financial support for the project “Linear Representation of Multiplicative Lie Algebra” (02011/19/2023/NBHM(R.P.)/R & D-II/5954).

Acknowledgements

We are thankful to Dr. Seema Kushwaha for her constant support.

References

[1] G. J. Ellis, On five well-known commutator identities, J. Austral. Math. Soc. Ser. A 54 (1993), no. 1, 1–19. 10.1017/S1446788700036934Search in Google Scholar

[2] A. Kumar, D. Pal, S. Kushwaha and S. K. Upadhyay, The Schur multiplier of some finite multiplicative Lie algebras, J. Lie Theory 34 (2024), no. 2, 423–436. Search in Google Scholar

[3] R. Lal and S. K. Upadhyay, Multiplicative Lie algebras and Schur multiplier, J. Pure Appl. Algebra 223 (2019), no. 9, 3695–3721. 10.1016/j.jpaa.2018.12.003Search in Google Scholar

[4] M. S. Pandey, R. Lal and S. K. Upadhyay, Lie commutator, solvability and nilpotency in multiplicative Lie algebras, J. Algebra Appl. 20 (2021), no. 8, Paper No. 2150138. 10.1142/S0219498821501383Search in Google Scholar

[5] M. S. Pandey and S. K. Upadhyay, Classification of multiplicative Lie algebra structures on a finite group, Colloq. Math. 168 (2022), no. 1, 25–34. 10.4064/cm8397-12-2020Search in Google Scholar

[6] F. Point and P. Wantiez, Nilpotency criteria for multiplicative Lie algebras, J. Pure Appl. Algebra 111 (1996), no. 1–3, 229–243. 10.1016/0022-4049(95)00115-8Search in Google Scholar

[7] G. L. Walls, Multiplicative Lie algebras, Turkish J. Math. 43 (2019), no. 6, 2888–2897. 10.3906/mat-1904-55Search in Google Scholar

Received: 2025-02-24
Revised: 2025-04-04
Accepted: 2025-04-19
Published Online: 2025-07-09

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 6.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/gmj-2025-2060/html?lang=en
Scroll to top button