Advanced search
Publication Cover
Communications in Algebra Volume 52, 2024 - Issue 1
Submit an article Journal homepage
95
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

The derivation algebra and automorphism group of the n-th Schrödinger algebra

Boqing LeiDepartment of Mathematics, Shanghai Maritime University, Shanghai, ChinaView further author information
&
Hengyun YangDepartment of Mathematics, Shanghai Maritime University, Shanghai, ChinaCorrespondence[email protected]
View further author information
Pages 283-294 | Received 04 Aug 2022, Accepted 12 Jul 2023, Published online: 28 Jul 2023

References

  • Ballesteros, A., Herranz, F. J., Parashar, P. (2000). (1 + 1) Schrödinger Lie bialgebras and their Poisson-Lie groups. J. Phys. A: Math. Gen. 33(17):3445–3465. DOI: 10.1088/0305-4470/33/17/304.
  • Bavula, V. V., Lu, T. (2018). Classification of simple weight modules over the Schrödinger algebra. Can. Math. Bull. 61(1):16–39. DOI: 10.4153/CMB-2017-017-7.
  • Bavula, V. V., Lu, T. (2018). The universal enveloping algebra of the Schrödinger algebra and its prime spectrum. Can. Math. Bull. 61(4):688–703. DOI: 10.4153/CMB-2018-009-1.
  • Cai, Y., Cheng, Y., Shen, R. (2014). Quasi-Whittaker modules for the Schrödinger algebra. Linear Algebra Appl. 463:16–32. DOI: 10.1016/j.laa.2014.09.001.
  • Cai, Y., Zhang, X. (2019). Simple singular Whittaker modules over the Schrödinger algebra. Commun. Math. Stat. 7(4):475–483. DOI: 10.1007/s40304-019-00180-9.
  • Chen, Z., Wang, Y. (2023). Derivations and biderivations of the n-th Schrödinger algebra. Commun. Algebra 51(3):1049–1062. DOI: 10.1080/00927872.2022.2122485.
  • Dubsky, B. (2014). Classification of simple weight modules with finite-dimensional weight spaces over the Schrödinger algebra. Linear Algebra Appl. 443:204–214. DOI: 10.1016/j.laa.2013.11.016.
  • Dobrev, V. K., Doebner, H. D., Mrugalla, C. (1997). Lowest weight representations of the Schrödinger algebra and generalized heat/Schrödinger equations. Rep. Math. Phys. 39(2):201–218. DOI: 10.1016/S0034-4877(97)88001-9.
  • Farnsteiner, R. (1988). Derivations and extensions of finitely generated graded Lie algebras. J. Algebra 118(1):34–45. DOI: 10.1016/0021-8693(88)90046-4.
  • Jacobson, N. (1979). Lie Algebras. New York: Dover Publications, Inc.
  • Shen, R., Jiang, C. (2006). The derivation algebra and automorphism group of the twisted Heisenberg-Virasoro algebra. Commun. Algebra 34(7):2547–2558. DOI: 10.1080/00927870600651257.
  • Tao, W. (2022). On simple modules of the n-th Schrödinger algebra. J. Pure Appl. Algebra 226(5):106944. DOI: 10.1016/j.jpaa.2021.106944.
  • Wu, Y. (2013). Finite dimensional indecomposable modules for Schrödinger algebra. J. Math. Phys. 54(7):073503. DOI: 10.1063/1.4812558.
  • Wu, Y., Zhu, L. (2013). Simple weight modules for Schrödinger algebra. Linear Algebra Appl. 438(1):559–563. DOI: 10.1016/j.laa.2012.07.029.
  • Wu, Q., Tang, X. (2022). Derivations and biderivations of the Schrödinger algebra in (n + 1)-dimensional space-time. Linear Multilinear Algebra 71(7):1–25. DOI: 10.1080/03081087.2022.2050884.
  • Wang, W., Li, J., Xu, Y. (2012). Derivations and automorphisms of twisted deformative Schrödinger-Virasoro Lie algebras. Commun. Algebra 40(9):3365–3388. DOI: 10.1080/00927872.2011.589090.
  • Yang, Y., Tang, X. (2018). Derivations of the Schrödinger algebra and their applications. J. Appl. Math. Comput. 58(1):567–576. DOI: 10.1007/s12190-017-1157-5.
  • Zhang, X., Cheng, Y. (2015). Simple Schrödinger modules which are locally finite over the positive part. J. Pure Appl. Algebra 219(7):2799–2815. DOI: 10.1016/j.jpaa.2014.09.029.
  • Zhang, H., Shao, W., Lu, C. (2007). The automorphism group of the Heisenberg Lie algebra. J. Capit. Nor. Univ. (Nat. Sci. Ed.) 28(1):1–14. DOI: 10.2307/2374228.

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.