Notes on a non-associative algebras with exponential functions III

Commun. Korean Math. Soc. 2008 Vol. 23, No. 2, 153-159 Printed June 1, 2008

Seul Hee Choi University of Jeonju

Abstract : For ${\Bbb F}[e^{\pm x}]_{\{\partial\}}$, all the derivations of the evaluation algebra ${\Bbb F}[e^{\pm x}]_{\{\partial\}}$ is found in the paper (see \cite{W}). For $M=\{\partial_1, \partial_1^2 \},$ $Der_{non}({\Bbb F}[e^{\pm x}]_M))$ of the evaluation algebra ${\Bbb F}[e^{\pm x},e^{\pm y}]_M$ is found in the paper (see \cite{C}). For $M=\{\partial_1^2, \partial_2^2 \},$ we find $Der_{non}({\Bbb F}[e^{\pm x}, e^{\pm y}]_M))$ of the evaluation algebra ${\Bbb F}[e^{\pm x},e^{\pm y}]_M$ in this paper.