Abstract
The present paper is devoted to study 2-local derivations on the Schrödinger algebra which is a finite-dimensional, non-semisimple and non-solvable Lie algebra. We first give a new example of 2-local derivation on the Heisenberg subalgebra of Schrödinger algebra which is not a derivation. Then we prove that every 2-local derivation on the Schrödinger algebra is a derivation.
Similar content being viewed by others
References
Ayupov, Sh.A., Kudaybergenov, K.K., Yusupov, B.B.: 2-local derivations on generalized Witt algebras. Linear Multilinear Algebra 69(16), 3130–3140 (2021)
Ayupov, Sh.A., Kudaybergenov, K.K., Rakhimov, I.S.: 2-local derivations on finite-dimensional Lie algebras. Linear Algebra Appl. 474, 1–11 (2015)
Ballesteros, A., Herranz, F., Parashar, P.: \((1+ 1)\) Schrödinger Lie bialgebras and their Poisson–Lie groups. J. Phys. A Math. Gen. 33(17), 3445–3665 (2000)
Bavula, V.V., Lu, T.: The universal enveloping algebra of the Schrödinger algebra and its prime spectrum. Can. Math. Bull. 61(4), 688–703 (2018)
Bergshoeff, E., Hartong, J., Rosseel, J.: Torsional Newton–Cartan geometry and the Schrödinger algebra. Class. Quant. Gravity 32(13), 135017 (2015)
Bresar, M.: On generalized biderivations and related maps. J. Algebra 172(3), 764–786 (1995)
Dobrev, V., Doebner, H., Mrugalla, C.: Lowest weight representations of the Schrödinger algebra and generalized heat/Schrödinger equations. Rep. Math. Phys. 39, 201–218 (1997)
Liu, G., Li, Y., Wang, K.: Irreducible weight modules over the Schrödinger Lie algebra in (n+1) dimensional space-time. J. Algebra 575(1), 1–13 (2021)
Perroud, M.: Projective representations of the Schrödinger group. Helv. Phys. Acta 50, 233–252 (1977)
Šemrl, P.: Local automorphisms and derivations on \(B(H)\). Proc. Am. Math. Soc. 125, 2677–2680 (1997)
Tang, X.: 2-Local derivations on the W-algebra W(2, 2). J. Algebra Appl. 20(12), 2150237 (2021)
Tang, X.: Biderivations of finite-dimensional complex simple Lie algebras. Linear Multilinear Algebra 66(2), 250–259 (2018)
Wu, Y., Zhu, L.: Simple weight modules for Schrödinger algebra. Linear Algebra Appl. 438, 559–563 (2013)
Yang, Y., Tang, X.: Derivations of the Schrödinger algebra and their applications. J. Appl. Math. Comput. 58(1–2), 567–576 (2018)
Zhao, Y., Chen, Y., Zhao, K.: 2-local derivations on Witt Algebras. J. Algebra Appl. 20(4), 2150068 (2021)
Acknowledgements
We would like to thank the referees for their invaluable omments and suggestions.
Funding
This work is supported in part by NNSF of China (No. 11771069), NSF of Heilongjiang Province (No. LH2020A020), the Found for the graduate innovation research of Heilongjiang University (No. YJSCX2021-211HLJU), and the fund of Heilongjiang Provincial Laboratory of the Theory and Computation of Complex Systems.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Ali Taherifar.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wu, Q., Tang, X. 2-Local Derivations on the Schrödinger Algebra. Bull. Iran. Math. Soc. 48, 3393–3404 (2022). https://doi.org/10.1007/s41980-022-00700-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41980-022-00700-4