Abstract
Every non-associative algebra L corresponds to its symmetric semi-Lie algebra <TEX>$L_{[,]}$</TEX> with respect to its commutator. It is an interesting problem whether the equality <TEX>$Aut{non}(L)=Aut_{semi-Lie}(L)$</TEX> holds or not [2], [13]. We find the non-associative algebra automorphism groups <TEX>$Aut_{non}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$</TEX> and <TEX>$Aut_{non-Lie}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$</TEX> where every automorphism of the automorphism groups is the composition of elementary maps [3], [4], [7], [8], [9], [10], [11]. The results of the paper show that the F-algebra automorphism groups of a polynomial ring and its Laurent extension make easy to find the automorphism groups of the algebras in the paper.
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