Advanced search
Publication Cover
Communications in Algebra Volume 47, 2019 - Issue 4
Submit an article Journal homepage
112
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length

Kobiljon K. AbdurasulovInstitute of Mathematics, Tashkent, Uzbekistan; View further author information
,
Jobir Q. AdashevInstitute of Mathematics, Tashkent, Uzbekistan; Correspondence[email protected]
View further author information
,
José M. CasasDepartment of Applied Mathematics I, E. E. Forestal, University of Vigo, Pontevedra, Spain; View further author information
&
Bakhrom A. OmirovNational University of Uzbekistan, Tashkent, UzbekistanView further author information
Pages 1578-1594 | Received 03 Apr 2018, Accepted 26 Jul 2018, Published online: 08 Jan 2019

References

  • Abdurasulov, K. K., Adashev, J. K., Sattarov, A. M. (2016). Solvable Leibniz algebras with 2-filiform nilradical. Uzbek Math. J. 4:16–23.
  • Barnes, D. W. (2012). On Levi’s theorem for Leibniz algebras. Bull. Aust. Math. Soc. 86(2):184–185.
  • Bosko-Dunbar, L., Dunbar, J. D., Hird, J. T., Stagg, K. (2015). Solvable leibniz algebras with heisenberg nilradical. Commun. Algebra. 43(6):2272–2281.
  • Cabezas, J. M., Camacho, L. M., Rodríguez, I. M. (2008). On filiform and 2-filiform Leibniz algebras of maximum length. J. Lie Theory. 18:335–350.
  • Camacho, L. M., Cañete, E. M., Gómez, J. R., Omirov, B. A. (2011). Quasi-filiform Leibniz algebras of maximum length. Sib. Math. J. 52(5):840–853.
  • Camacho, L. M., Omirov, B. A., Masutova, K. K. (2016). Solvable Leibniz algebras with filiform nilradical. Bull. Malays. Math. Sci. Soc. 39(1):283–303.
  • Casas, J. M., Ladra, M., Omirov, B. A., Karimjanov, I. A. (2013). Classification of solvable leibniz algebras with null-filiform nilradical. Linear Mult. Alg. 61(6):758–774.
  • Casas, J. M., Ladra, M., Omirov, B. A., Karimjanov, I. A. (2013). Classiication of solvable Leibniz algebras with naturally graded filiform nilradical. Linear Alg. Appl. 438(7):2973–3000.
  • Karimjanov, I. A., Khudoyberdiyev, A. K., Omirov, B. A. (2015). Solvable Leibniz algebras with triangular nilradicals. Linear Alg. Appl. 466:530–546.
  • Khalkulova, K. A., Ladra, M., Omirov, B. A., Sattorov, A. M. (2018). Solvable Leibniz algebras with quasi-filiform Lie algebras of maximum length nilradicals:15, arXiv:18.01.08935v1.
  • Khudoyberdiyev, A. K., Ladra, M., Omirov, B. A. (2014). On solvable Leibniz algebras whose nilradical is a direct sum of null-filiform algebras. Linear Mult. Alg. 62(9):1220–1239.
  • Ladra, M., Masutova, K. K., Omirov, B. A. (2016). Corrigendum to “classification of solvable Leibniz algebras with naturally graded filiform nilradical” [linear alg. Appl. 438 (7) (2013) 2973–3000]. Linear Alg. Appl. 507:513–517.
  • Loday, J.-L. (1993). Une version non commutative des algèbres de lie: les algèbres de leibniz. Enseign. Math. 39(3–4):269–293.
  • Malcev, A. I. (1950). Solvable lie algebras. Amer. Math. Soc. Trans. 27:36.
  • Mubarakzjanov, G. M. (1963). On solvable lie algebras (Russian). Izv. Vysš. Učehn. Zaved. Matematika. 32(1):114–123.
  • Ndogmo, J. C., Winternitz, P. (1994). Solvable lie algebras with Abelian nilradicals. J. Phys. A: Math. Gen. A. 27(2):405–423.
  • Rubin, J. L., Winternitz, P. (1993). Solvable lie algebras with Heisenberg ideals. J. Phys. A: Math. Gen. A. 26(5):1123–1138.
  • Shabanskaya, A. (2017). Solvable extensions of naturally graded quasi-filiform leibniz algebras of second type L1 and L3. Comm. Algebra. 45(10):4492–4520.
  • Shabanskaya, A. (2016). Solvable indecomposable extensions of two nilpotent Lie algebras. Commun. Algebra. 44(8):3626–3667.
  • Šnobl, L., Winternitz, P. (2005). A class of solvable lie algebras and their casimir invariants. J. Phys. A: Math. Gen. A. 38(12):2687–2700.
  • Šnobl, L., Winternitz, P. (2009). All solvable extensions of a class of nilpotent lie algebras of dimension n and degree of nilpotency n−1. J. Phys. A: Math. Theor. A. 42(10):105201.
  • Tremblay, S., Winternitz, P. (1998). Solvable Lie algebras with triangular nilradicals. J. Phys. A: Math. Gen. A. 31(2):789–806.
  • Wang, Y., Lin, J., Deng, S. (2008). Solvable Lie algebras with quasifiliform nilradicals. Comm. Algebra. 36(11):4052–4067.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.