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Linear and Multilinear Algebra Volume 71, 2023 - Issue 7
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Research Article

Derivations and Biderivations of the Schrödinger algebra in (n + 1)-dimensional space-time

Qingyan WuSchool of Mathematical Science, Heilongjiang University, Harbin, People's Republic of ChinaView further author information
&
Xiaomin TangSchool of Mathematical Science, Heilongjiang University, Harbin, People's Republic of ChinaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-9054-1286View further author information
ORCID Icon
Pages 1073-1097 | Received 03 Dec 2021, Accepted 20 Jan 2022, Published online: 17 Mar 2022

References

  • Brešar M. On generalized biderivations and related maps. J Algebra. 1995;172:764–786.
  • Chen Z. Biderivations and linear commuting maps on simple generalized Witt algebras over a field. Electron J Linear Algebra. 2016;31:1–12.
  • Chen Z, Yu Y. Biderivations and strong commutativity-preserving maps on parabolic subalgebras of simple Lie algebras. Linear Multilinear Algebra. 2020;1–13. doi:10.1080/03081087.2020.1809621.
  • Ding Z, Tang X. Biderivations of the galilean conformal algebra and their applications. Quaest Math. 2019;42(6):831–839.
  • Han X, Wang D, Xia C. Linear commuting maps and biderivations on the Lie algebras W(a,b). J Lie Theory. 2016;26:777–786.
  • Tang X. Biderivations of finite-dimensional complex simple Lie algebras. Linear Multilinear Algebra. 2018;66(2):250–259.
  • Tang X. Biderivations, linear commuting maps and commutative post-Lie algebra structures on W-algebras. Commun Algebra. 2017;45:5252–5261.
  • Wang D, Yu X. Biderivations and linear commuting maps on the Schrödinger-Virasoro Lie algebra. Commun Algebra. 2013;41:2166–2173.
  • Wang D, Yu X, Chen Z. Biderivations of the parabolic subalgebras of simple Lie algebras. Commun Algebra. 2011;39:4097–4104.
  • Chang Y, Chen L. Biderivations and linear commuting maps on the restricted Cartan-type Lie algebras W(n;1_) and S(n;1_). Linear Multilinear Algebra. 2019;67(8):1625–1636.
  • Chang Y, Chen L, Zhou X. Biderivations and linear commuting maps on the restricted Cartan-type Lie algebras H(n;1_). Commun Algebra. 2019;47(3):1311–1326.
  • Chang Y, Chen L, Zhou X. Biderivations and linear commuting maps on the restricted contact Lie algebras K(n;1_). Quaest Math. 2021;44(11):1529–1540.
  • Perroud M. Projective representations of the Schrödinger group. Helv Phys Acta. 1997;50:233–252.
  • Dobrev V, Doebner H, Mrugalla C. Lowest weight representations of the Schrödinger algebra and generalized heat/Schrödinger equations. Rep Math Phys. 1997;39:201–218.
  • Aizawa N, Dobrev V. Intertwining operator realization of non-relativistic holography. Nuclear Phys B. 2010;828:581–593.
  • Yang Y, Tang X. Derivation of the Schrödinger algebra and their applications. J Appl Math Comput. 2018;58(1-2):567–576.
  • Zhang X, Cheng Y. Simple Schrödinger modules which are locally finite over the positive part. J Pure Appl Algebra. 2015;219:2799–2815.
  • Liu G, Li Y, Wang K. Irreducible weight modules over the Schrödinger Lie algebra in (n+1) dimensional space-time. J Algebra. 2021;575(1):1–13.
  • Liu X, Guo X, Zhao K. Biderivations of the block Lie algebras. Linear Algebra Appl. 2018;538:43–55.
  • Posner E. Derivations in prime rings. Proc Amer Math Soc. 1957;8:1093–1100.
  • Brešar M. Commuting maps: a survey. Taiwanese J Math. 2004;8:361–397.
  • Vallette B. Homology of generalized partition posets. J Pure Appl Algebra. 2007;208:699–725.
  • Burde D, Dekimpe K, Vercammen K. Affine actions on Lie groups and post-Lie algebra structures. Linear Algebra Appl. 2012;437:1250–1263.
  • Burde D, Moens W. Commutative post-Lie algebra structures on Lie algebras. J Algebra. 2016;467:183–201.
  • Burde D, Dekimpe K, Moens W. Commutative post-Lie algebra structures and linear equations for nilpotent Lie algebras. J Algebra. 2019;526:12–29.

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