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Communications in Algebra Volume 52, 2024 - Issue 10
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Research Article

Local and 2-local Lie n-derivations of triangular algebras

Xingpeng ZhaoDepartment of Mathematics, Taiyuan University of Technology, Taiyuan, P.R. ChinaCorrespondence[email protected]
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Pages 4388-4398 | Received 27 Dec 2023, Accepted 15 Apr 2024, Published online: 02 May 2024

References

  • Abdullaev, I. Z. (1992). n− Lie derivations on von Neumann algebras. Uzbek. Mat. Zh. 5–6:3–9.
  • Ayupov, S., Kudaybergenov, K. (2015). 2-Local derivations on von Neumann algebras. Positivity 19:445–455. DOI: 10.1007/s11117-014-0307-3.
  • Benkovič, D., Eremita, D. (2004). Commuting traces and commutativity preserving maps on triangular algebras. J. Algebra 280:797–824. DOI: 10.1016/j.jalgebra.2004.06.019.
  • Benkovič, D., Eremita, D. (2012). Multiplicative Lie n-derivations of triangular rings. Linear Algebra Appl. 436:4224–4240. DOI: 10.1016/j.laa.2012.01.022.
  • Cheung, W. (2003). Lie derivations of triangular algebras. Linear Multilinear Algebra 51:299–310. DOI: 10.1080/0308108031000096993.
  • Crist, R. L. (1996). Local derivations on operator algebras. J. Funct. Anal. 135:76–92. DOI: 10.1006/jfan.1996.0004.
  • Fošner, A., Wei, F., Xiao, Z. (2013). Nonlinear Lie-type derivations of von Neumann algebras and related topics. Colloq. Math., 132:53–71.
  • Ji, P. S., Qi, W. Q. (2011). Characterizations of Lie derivations of triangular algebras. Linear Algebra Appl. 435:1137–1146. DOI: 10.1016/j.laa.2011.02.048.
  • Jing, W. (1997). Local derivations of reflexive algebras. Proc. Amer. Math. Soc. 125:869–873.
  • Johnson, B. E. (2000). Local derivations on C ∗-algebras are derivations. Trans. Amer. Math. Soc. 353:313–325.
  • Larson, D. R., Sourour, A. R. (1990). Local derivations and local automorphisms of B(X). Proc. Sympos. Pure Math. 51:187–194.
  • Li, C. J., Lu, F. Y. (2016). 2-Local ∗-Lie isomorphisms of operator algebras. Aequat. Math., 90:905–916.
  • Li, C. J., Lu, F. Y. (2016). 2-local Lie isomorphisms of nest algebras. Oper. Matrices 10:425–434. DOI: 10.7153/oam-10-24.
  • Liu, D., Zhang, J. H. (2017). Local Lie derivations on certain operator algebras. Ann. Funct. Anal. 8:270–280. DOI: 10.1215/20088752-0000012X.
  • Kadison, R. V. (1990). Local derivations. J. Algebra 130:494–509. DOI: 10.1016/0021-8693(90)90095-6.
  • Kim, S., Kim, J. (2004). Local automorphisms and derivations on Mn. Proc. Amer. Math. Soc. 132:1389–1392.
  • Šemrl, P. (1997). Local automorphisms and derivations on B(H). Proc. Amer. Math. Soc. 125:2677–2680.
  • Wang, Y. (2014). Lie n-derivations of unital algebras with idempotents. Linear Algebra Appl. 458:512–525. DOI: 10.1016/j.laa.2014.06.029.
  • Xiao, Z. K., Yang, Y. P. (2020). Lie n-derivations of incidence algebras. Commun. Algebra 48:105–118. DOI: 10.1080/00927872.2019.1632334.
  • Zhao, X. P. (2023). 2-Local Lie triple isomorphisms of nest algebras. Commun. Algebra 51:3756–3763. DOI: 10.1080/00927872.2023.2187637.
  • Zhao, X. P. (2023). Nonlinear Lie triple derivations by local actions on triangular algebras. J. Algebra Appl. 22:2350059-1-2350059-15. DOI: 10.1142/S0219498823500597.
  • Zhao, X. P. (2024). Nonlinear 2-local Lie n-derivations of von Neumann algebras. Commun. Algebra 52:1457–1465. DOI: 10.1080/00927872.2023.2263082.

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