138
Views
3
CrossRef citations to date
0
Altmetric
Research Article

Detecting capable Lie superalgebras

, &
Pages 4274-4290 | Received 04 Jun 2020, Accepted 04 Apr 2021, Published online: 19 May 2021

References

  • Alamian, V., Mohammadzadeh, H., Salemkar, A. R. (2008). Some properties of the Schur multiplier and covers of Lie algebras. Commun. Algebra 36:607–707.
  • Baer, R. (1938). Groups with preassigned central and central quotient group. Trans. Amer. Math. Soc. 44( 3):387–412. DOI: 10.1090/S0002-9947-1938-1501973-3.
  • Batten, P. (1993). Multipliers and covers of Lie algebras. Ph.D. Thesis. Raleigh, NC: North Carolina State University.
  • Batten, P., Stitzinger, E. (1996). On covers of Lie algebras. Commun. Algebra 24(14):4301–4317. DOI: 10.1080/00927879608825816.
  • Batten, P., Moneyhun, K., Stitzinger, E. (1996). On characterizing nilpotent Lie algebra by their multipliers. Commun. Algebra 24(14):4319–4330. DOI: 10.1080/00927879608825817.
  • Beyl, F., Felgner, U., Schmid, P. (1979). On groups occurring as center factor groups. J. Algebra 61(1):161–177. DOI: 10.1016/0021-8693(79)90311-9.
  • Brown, R., Loday, J. L. (1987). Van Kampen theorems for diagrams of spaces. Topology 26(3):311–821. DOI: 10.1016/0040-9383(87)90004-8.
  • Ellis, G. (1987). Non-abelian exterior products of Lie algebras and an exact sequence in the homology of Lie algebras. J. Pure Appl. Algebra 46( 2–3):111–115. DOI: 10.1016/0022-4049(87)90088-0.
  • Ellis, G. (1991). A non-abelian tensor products of Lie algebras, Glasgow Math. J. 33(1):101–120. DOI: 10.1017/S0017089500008107.
  • Ellis, G. (1995). Tensor products and q-cross modules. J. London Math. Soc. 51:241–258.
  • García-Martínez, X., Khmaladze, E., Ladra, M. (2015). Non-abelian tensor product and homology of Lie superalgebras. J. Algebra 440:464–488. DOI: 10.1016/j.jalgebra.2015.05.027.
  • Hardy, P., Stitzinger, E. (1998). On characterizing nilpotent Lie algebras by their multipliers t(L)=3,4,5,6. Commun. Algebra 26:3527–3539.
  • Hardy, P. (2005). On characterizing nilpotent Lie algebras by their multipliers III. Commun. Algebra 33( 11):4205–4210. DOI: 10.1080/00927870500261512.
  • Kac, V. G. (1977). Lie superalgebras. Adv. Math. 26(1):8–96. DOI: 10.1016/0001-8708(77)90017-2.
  • Moneyhun, K. (1994). Isoclinisms in Lie algebras. Algebras Groups Geom. 11:9–22.
  • Musson, I. (2012). Lie superalgebras and enveloping algebras. In: Graduate Studies in Mathematics, Vol. 131, Providence, RI: Amer. Math. Soc.
  • Nayak, S. (2018). Isoclinisim in Lie superalgebra. arXiv:1804.10434.
  • Nayak, S. (2019). Multipliers of nilpotent Lie superalgebras. Commun. Algebra 47(2), 689–705. DOI: 10.1080/00927872.2018.1492595.
  • Nayak, S., Padhan, R. N., Pati, K. C. (2020). Some properties of isoclinism in Lie superalgebras. Commun. Algebra 48(2):523–537. DOI: 10.1080/00927872.2019.1648654.
  • Nayak, S. (2021). Classification of finite dimensional nilpotent Lie superalgebras by their multiplier. J. Lie Theory 31(2):439–458.
  • Niroomand, P., Russo, F. G. (2011). A note on the Schur multiplier of a nilpotent Lie algebra. Commun. Algebra 39( 4):1293–1297. DOI: 10.1080/00927871003652660.
  • Niroomand, P., Russo, F. G. (2011). A restriction on the Schur multiplier of a nilpotent Lie algebras. Electron. J. Linear Algebra 22:1–9.
  • Niroomand, P. (2011). On the dimension of the Schur multiplier of nilpotent Lie algebras. Centr. Eur. J. Math. 9( 1):57–64. DOI: 10.2478/s11533-010-0079-3.
  • Niroomand, P., Parvizi, M., Russo, F. G. (2013). Some criteria for detecting capable Lie algebras. J. Algebra 384:36–44. DOI: 10.1016/j.jalgebra.2013.02.033.
  • Rodriguez-Vallarte, M. C., Salgado, G., Sanchez-Valenzuela, O. A. (2011). Heisenberg Lie superalgebras and their invariant superorthogonal and supersympletic forms. J. Algebra 332(1):71–86. DOI: 10.1016/j.jalgebra.2011.02.003.

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:

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:

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.