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Research Article

Characterizations of derivations on incidence algebras by local actions

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Received 28 Jan 2024, Accepted 15 Apr 2024, Published online: 06 May 2024

References

  • Albeverio, S., Ayupov, Sh. A., Kudaybergenov, K. K., Nurjanov, B. O. (2011). Local derivations on algebras of measurable operators. Commun. Contemp. Math. 13:643–657. DOI: 10.1142/S0219199711004270.
  • Ayupov, Sh. A., Kudaybergenov, K. K., Omirov, B. A. (2020). Local and 2-local derivations and automorphisms on simple Leibniz algebras. Bull. Malays. Math. Sci. Soc. 43:2199–2234. DOI: 10.1007/s40840-019-00799-5.
  • Brešar, M. (1992). Characterizations of derivations on some normed algebras with involution. J. Algebra 152:454–462. DOI: 10.1016/0021-8693(92)90043-L.
  • Brešar, M. (2007). Characterizing homomorphisms, derivations and multipliers in rings with idempotents. Proc. Roy. Soc. Edinburgh Sect. A 137:9–21. DOI: 10.1017/S0308210504001088.
  • Brešar, M. (2016). Finite dimensional zero product determined algebras are generated by idempotents. Expo. Math. 34:130–143. DOI: 10.1016/j.exmath.2015.07.002.
  • Brešar, M. (2021). Zero Product Determined Algebras. Cham: Springer Nature.
  • Chebotar, M. A., Ke, W.-F., and Lee, P.-H. (2004). Maps characterized by action on zero products. Pacific J. Math. 216:217–228. DOI: 10.2140/pjm.2004.216.217.
  • Crist, R. L. (1996). Local derivations on operator algebras. J. Funct. Anal. 135:76–92. DOI: 10.1006/jfan.1996.0004.
  • Ben Ali Essaleh, A., Peralta, A. M. (2018). Linear maps on C * -algebras which are derivations or triple derivations at a point. Linear Algebra Appl. 538:1–21.
  • Hadwin, D., Li, J. K. (2004). Local derivations and local automorphisms. J. Math. Anal. Appl. 290:702–714. DOI: 10.1016/j.jmaa.2003.10.015.
  • Herstein, I. N. (1961). Lie and Jordan structures in simple, associative rings. Bull. Amer. Math. Soc. 67:517–531. DOI: 10.1090/S0002-9904-1961-10666-6.
  • Hou, J. C., Qi, X. F. (2008). Additive maps derivable at some points on J -subspace lattice algebras. Linear Algebra Appl. 429:1851–1863.
  • Jia, H. Y., Xiao, Z. K. (2020). Commuting maps on certain incidence algebras. Bull. Iran. Math. Soc. 46:755–765. DOI: 10.1007/s41980-019-00289-1.
  • Jing, W., Lu, S. J., Li, P. T. (2002). Characterization of derivations on some operator algebras. Bull. Aust. Math. Soc. 66:227–232. DOI: 10.1017/S0004972700040077.
  • Johnson, B. E. (2001). Local derivations on C*-algebras are derivations. Trans. Amer. Math. Soc. 353:313–325.
  • Kadison, R. (1990). Local derivations. J. Algebra 130:494–509. DOI: 10.1016/0021-8693(90)90095-6.
  • Kaygorodov, I., Khrypchenko, M. (2021). Poisson structures on finitary incidence algebras. J. Algebra 578:402–420. DOI: 10.1016/j.jalgebra.2021.03.011.
  • Khrypchenko, M. (2018). Local derivations of finitary incidence algebras. Acta Math. Hungar. 154:48–55. DOI: 10.1007/s10474-017-0758-7.
  • Koppinen, M. (1995). Automorphisms and higher derivations of incidence algebras. J. Algebra 174:698–723. DOI: 10.1006/jabr.1995.1147.
  • Larson, D. R., Sourour, A. R. (1990). Local Derivations and Local Automorphisms of B(X). In: Proceedings of Symposia in Pure Mathematics, 51, Providence, Rhode Island 1990, Part 2, pp. 187–194.
  • Nowicki, A., Nowosad, I. (2004). Local derivations of subrings of matrix rings. Acta Math. Hungar. 105:145–150. DOI: 10.1023/B:AMHU.0000045539.32024.db.
  • Spiegel, E., O’Donnell, C. (1997). Incidence Algebras. Monographs and Textbooks in Pure and Applied Mathematics, Vol. 206. New York: Marcel Dekker.
  • Wang, D. N., Xiao, Z. K. (2019). Lie triple derivations of incidence algebras. Commun. Algebra 47:1841–1852. DOI: 10.1080/00927872.2018.1523422.
  • Wu, J. (1997). Local derivations of reflexive algebras. Proc. Amer. Math. Soc. 125:869–873. DOI: 10.1090/S0002-9939-97-03720-9.
  • Wu, J. (2001). Local derivations of reflexive algebras II. Proc. Amer. Math. Soc. 129:1733–1737. DOI: 10.1090/S0002-9939-01-05792-6.
  • Xiao, Z. K. (2015). Jordan derivations of incidence algebras. Rocky Mountain J. Math. 45:1357–1368. DOI: 10.1216/RMJ-2015-45-4-1357.
  • Zhang, X., Khrypchenko, M. (2017). Lie derivations of incidence algebras. Linear Algebra Appl. 513:69–83. DOI: 10.1016/j.laa.2016.10.011.

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