Version 1
: Received: 10 April 2024 / Approved: 10 April 2024 / Online: 10 April 2024 (10:09:03 CEST)
How to cite:
Varshney, V.; Alali, A.S.; Ali, S. Linear Generalized N-derivations on C-algebras*. Preprints2024, 2024040728. https://doi.org/10.20944/preprints202404.0728.v1
Varshney, V.; Alali, A.S.; Ali, S. Linear Generalized N-derivations on C-algebras*. Preprints 2024, 2024040728. https://doi.org/10.20944/preprints202404.0728.v1
Varshney, V.; Alali, A.S.; Ali, S. Linear Generalized N-derivations on C-algebras*. Preprints2024, 2024040728. https://doi.org/10.20944/preprints202404.0728.v1
APA Style
Varshney, V., Alali, A.S., & Ali, S. (2024). Linear Generalized N-derivations on C-algebras*. Preprints. https://doi.org/10.20944/preprints202404.0728.v1
Chicago/Turabian Style
Varshney, V., Amal S. Alali and Shakir Ali. 2024 "Linear Generalized N-derivations on C-algebras*" Preprints. https://doi.org/10.20944/preprints202404.0728.v1
Abstract
Let $n \geq 2$ be a fixed integer and $\mathcal{A}$ be a $C^*$-algebra. A permuting $ n $-linear map $ \mathcal{G} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ is known to be symmetric generalized $n$-derivation if there exists a symmetric $n$-derivation $ \mathfrak{D} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ such that $ \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i} x_{i}^{\prime}, \ldots, x_{n}\right)= \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i}, \ldots, x_{n}\right) x_{i}^{\prime}+x_{i} \mathfrak{D} (x_{1}, x_{2},\ldots, x_{i}^{\prime}, \ldots, x_{n})$ holds for all $x_{i}, x_{i}^{\prime} \in \mathcal{A} $. In this paper, we investigate the structure of $C^*$-algebras involving generalized linear $n$-derivations. Moreover, we describe the forms of traces of linear $n$-derivations satisfying certain functional identity.
Keywords
Linear derivation; linear n-derivation; generalized linear n-derivation; Lie ideal; Banach algebra; C*-algebra
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
