Abstract:
Given a finite-dimensional associative commutative algebra $A$ over a field $F$, we define the structure of a Lie algebra using a nonzero derivation $D$ of $A$. If $A$ is a field and $\operatorname{char}F>3$; then the corresponding algebra is simple, presenting a nonisomorphic analog of the Zassenhaus algebra $W_1(m)$.
Keywords:simple Lie algebra, field derivation, Zassenhaus algebra, $A$-algebra.
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