1
Department of Science, University of Birjand, P.O. Box 414, Birjand 9717851367, Birjand, Iran
2
Department of Science, University of Birjand, P.O. Box 414, Birjand 9717851367, Birjand, Iran
3
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Mashhad, Iran
Abstract
Let $\mathcal{A}$ be a $C^*$-algebra and $Z(\mathcal{A})$ the center of $\mathcal{A}$. A sequence $\{L_{n}\}_{n=0}^{\infty}$ of linear mappings on $\mathcal{A}$ with $L_{0}=I$, where $I$ is the identity mapping
on $\mathcal{A}$, is called a Lie higher derivation if $L_{n}[x,y]=\sum_{i+j=n} [L_{i}x,L_{j}y]$ for all $x,y \in
\mathcal{A}$ and all $n\geqslant0$. We show that $\{L_{n}\}_{n=0}^{\infty}$ is a Lie higher derivation if and only if there exist a higher derivation $\{D_{n}:\mathcal{A}\rightarrow\mathcal{A}\}_{n=0}^{\infty}$ and a sequence of linear mappings $\{\Delta_{n}:\mathcal{A}\rightarrow Z(\mathcal{A})\}_{n=0}^{\infty}$ such that $\Delta_0=0$, $\Delta_n([x,y])=0$ and $L_n=D_n+\Delta_n$ for every $x,y\in\mathcal{A}$ and all $n\geq0$.
Janfada, A. R., Saidi, H., & Mirzavaziri, M. (2015). Characterization of Lie higher Derivations on $C^{*}$-algebras. Bulletin of the Iranian Mathematical Society, 41(4), 901-906.
MLA
Janfada, A. R., Saidi, H., & Mirzavaziri, M. "Characterization of Lie higher Derivations on $C^{*}$-algebras", Bulletin of the Iranian Mathematical Society, 41, 4, 2015, 901-906.
HARVARD
Janfada A. R., Saidi H., Mirzavaziri M. (2015). 'Characterization of Lie higher Derivations on $C^{*}$-algebras', Bulletin of the Iranian Mathematical Society, 41(4), pp. 901-906.
CHICAGO
A. R. Janfada, H. Saidi & M. Mirzavaziri, "Characterization of Lie higher Derivations on $C^{*}$-algebras," Bulletin of the Iranian Mathematical Society, 41 4 (2015): 901-906,
VANCOUVER
Janfada A. R., Saidi H., Mirzavaziri M. Characterization of Lie higher Derivations on $C^{*}$-algebras. BIMS. 2015;41(4):901-906.
