Browse > Article
http://dx.doi.org/10.4134/BKMS.b200850

CHARACTERIZATION OF LIE TYPE DERIVATION ON VON NEUMANN ALGEBRA WITH LOCAL ACTIONS  

Ashraf, Mohammad (Department of mathematics Aligarh Muslim University)
Jabeen, Aisha (Department of Applied Sciences & Humanities Jamia Millia Islamia)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.5, 2021 , pp. 1193-1208 More about this Journal
Abstract
Let 𝓐 be a von Neumann algebra with no central summands of type I1. In this article, we study Lie n-derivation on von Neumann algebra and prove that every additive Lie n-derivation on a von Neumann algebra has standard form at zero product as well as at projection product.
Keywords
Derivation; von Neumann algebra; Lie type derivation; commutator;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 M. Bresar and C. R. Miers, Commutativity preserving mappings of von Neumann algebras, Canad. J. Math. 45 (1993), no. 4, 695-708. https://doi.org/10.4153/CJM-1993-039-x   DOI
2 R. V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator algebras. Vol. I, Pure and Applied Mathematics, 100, Academic Press, Inc., New York, 1983.
3 F. Lu and W. Jing, Characterizations of Lie derivations of B(X), Linear Algebra Appl. 432 (2010), no. 1, 89-99. https://doi.org/10.1016/j.laa.2009.07.026   DOI
4 X. Qi, Characterization of (generalized) Lie derivations on J-subspace lattice algebras by local action, Aequationes Math. 87 (2014), no. 1-2, 53-69. https://doi.org/10.1007/s00010-012-0177-3   DOI
5 X. Qi and J. Ji, Characterizing derivations on von Neumann algebras by local actions, J. Funct. Spaces Appl. 2013 (2013), Art. ID 407427, 11 p. https://doi.org/10.1155/2013/407427   DOI
6 Y. Wang, Lie n-derivations of unital algebras with idempotents, Linear Algebra Appl. 458 (2014), 512-525. https://doi.org/10.1016/j.laa.2014.06.029   DOI
7 M. Ashraf and A. Jabeen, Characterizations of additive ξ-Lie derivations on unital algebras, Ukrainian Math. J. 73 (2021), no. 4, 455-466. https://doi.org/10.37863/umzh.v73i4.838   DOI
8 X. Qi and J. Hou, Characterization of Lie derivations on von Neumann algebras, Linear Algebra Appl. 438 (2013), no. 1, 533-548. https://doi.org/10.1016/j.laa.2012.08.019   DOI
9 X. Qi, Characterizing Lie n-derivations for reflexive algebras, Linear Multilinear Algebra 63 (2015), no. 8, 1693-1706. https://doi.org/10.1080/03081087.2014.968519   DOI
10 I. Z. Abdullaev, n-Lie derivations on von Neumann algebras, Uzbek. Mat. Zh. No. 5-6 (1992), 3-9.
11 P. Ji and W. Qi, Characterizations of Lie derivations of triangular algebras, Linear Algebra Appl. 435 (2011), no. 5, 1137-1146. https://doi.org/10.1016/j.laa.2011.02.048   DOI
12 P. Ji, W. Qi, and X. Sun, Characterizations of Lie derivations of factor von Neumann algebras, Linear Multilinear Algebra 61 (2013), no. 3, 417-428. https://doi.org/10.1080/03081087.2012.689982   DOI
13 L. Liu, Lie triple derivations on factor von Neumann algebras, Bull. Korean Math. Soc. 52 (2015), no. 2, 581-591. https://doi.org/10.4134/BKMS.2015.52.2.581   DOI
14 L. Liu, Lie triple derivations on von Neumann algebras, Chin. Ann. Math. Ser. B 39 (2018), no. 5, 817-828. https://doi.org/10.1007/s11401-018-0098-0   DOI
15 C. R. Miers, Lie homomorphisms of operator algebras, Pacific J. Math. 38 (1971), 717-735. http://projecteuclid.org/euclid.pjm/1102969919   DOI
16 Y. Wang and Y. Wang, Multiplicative Lie n-derivations of generalized matrix algebras, Linear Algebra Appl. 438 (2013), no. 5, 2599-2616. https://doi.org/10.1016/j.laa.2012.10.052   DOI