Nonlinear ∗-Lie Higher Derivations of Unital ∗-Algebras

Mohammad Ashraf; Jehad Jumah Al Jaraden; Mohammad Afajal Ansari; Md Shamim Akhter

doi:10.1007/978-981-97-6798-4_26

Nonlinear ∗-Lie Higher Derivations of Unital ∗-Algebras

Mohammad Ashraf^*
, Jehad Jumah Al Jaraden
, Mohammad Afajal Ansari
, Md Shamim Akhter

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Let A be a unital ∗-algebra and L = {L_n}_n_∈N be a nonlinear ∗-Lie higher derivation on A. In the present paper, it is shown that under some appropriate assumptions L is proper, that is, for each n ∈ N, L_n: A → A has the form L_n = d_n + T_n, where {d_n}_n_∈N is an additive ∗-higher derivation on A and {T_n}_n_∈N is a family of mappings T_n: A → Z(A) such that T_n([x, y]) = 0 for all x, y ∈ A, n ∈ N.

Original language	English
Title of host publication	Algebra and Its Applications - ICAA-2023
Editors	Manoj Kumar Patel, Mohammad Ashraf, Najib Mahdou, Hwankoo Kim
Publisher	Springer
Pages	315-331
Number of pages	17
ISBN (Print)	9789819767977
DOIs	https://doi.org/10.1007/978-981-97-6798-4_26
State	Published - 2025
Externally published	Yes
Event	International Conference on Algebra and its Applications, ICAA 2023 - Fez, Morocco Duration: 11 Jul 2023 → 14 Jul 2023

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	474
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Algebra and its Applications, ICAA 2023
Country/Territory	Morocco
City	Fez
Period	11/07/23 → 14/07/23

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

Keywords

Unital ∗-algebras
∗-derivation
∗-Lie derivation
∗-Lie higher derivation

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-981-97-6798-4_26

Cite this

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title = "Nonlinear ∗-Lie Higher Derivations of Unital ∗-Algebras",

abstract = "Let A be a unital ∗-algebra and L = \{Ln\}n∈N be a nonlinear ∗-Lie higher derivation on A. In the present paper, it is shown that under some appropriate assumptions L is proper, that is, for each n ∈ N, Ln: A → A has the form Ln = dn + Tn, where \{dn\}n∈N is an additive ∗-higher derivation on A and \{Tn\}n∈N is a family of mappings Tn: A → Z(A) such that Tn([x, y]) = 0 for all x, y ∈ A, n ∈ N.",

keywords = "Unital ∗-algebras, ∗-derivation, ∗-Lie derivation, ∗-Lie higher derivation",

author = "Mohammad Ashraf and \{Al Jaraden\}, \{Jehad Jumah\} and Ansari, \{Mohammad Afajal\} and Akhter, \{Md Shamim\}",

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year = "2025",

doi = "10.1007/978-981-97-6798-4\_26",

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isbn = "9789819767977",

series = "Springer Proceedings in Mathematics and Statistics",

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Ashraf, M, Al Jaraden, JJ, Ansari, MA & Akhter, MS 2025, Nonlinear ∗-Lie Higher Derivations of Unital ∗-Algebras. in MK Patel, M Ashraf, N Mahdou & H Kim (eds), Algebra and Its Applications - ICAA-2023. Springer Proceedings in Mathematics and Statistics, vol. 474, Springer, pp. 315-331, International Conference on Algebra and its Applications, ICAA 2023, Fez, Morocco, 11/07/23. https://doi.org/10.1007/978-981-97-6798-4_26

Nonlinear ∗-Lie Higher Derivations of Unital ∗-Algebras. / Ashraf, Mohammad; Al Jaraden, Jehad Jumah; Ansari, Mohammad Afajal et al.
Algebra and Its Applications - ICAA-2023. ed. / Manoj Kumar Patel; Mohammad Ashraf; Najib Mahdou; Hwankoo Kim. Springer, 2025. p. 315-331 (Springer Proceedings in Mathematics and Statistics; Vol. 474).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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