Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2021; 58(5): 1193-1208

Online first article August 26, 2021      Printed September 30, 2021

https://doi.org/10.4134/BKMS.b200850

Copyright © The Korean Mathematical Society.

Characterization of Lie type derivation on von Neumann algebra with local actions

Mohammad Ashraf, Aisha Jabeen

Aligarh Muslim University; Jamia Millia Islamia

Abstract

Let $\mathcal{A}$ be a von Neumann algebra with no central summands of type $I_1.$ 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

MSC numbers: 47B47, 47L10

Supported by: The first author is partially supported by MATRICS research grant from DST(SERB)(MTR/2017/000033). Also, this work has been sponsored by Dr. D. S. Kothari Postdoctoral Fellowship (Award letter No. F.4-2/2006(BSR)/MA/18-19/0014) awarded to the second author under the University Grants Commission, Government of India, New Delhi.