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Every non-associative algebra $L${\hskip-0.015cm} corresponds to
its symmetric semi-Lie algebra $L_{[,]}$ with respect to its
commutator. It is an interesting problem whether the equality
{\tiny$Aut_{non}(L){\hskip-0.03cm}={\hskip-0.03cm}Aut_{semi-Lie}(L)$}
holds or not \cite{Al}, \cite{San}. We find the non-associative
algebra automorphism groups $Aut_{non}$ $(\overline {WN_{0,0,1}}_
{[0,1,r_1,\ldots ,r_p]} )$ and $Aut_{semi-Lie}$ $(\overline
{WN_{0,0,1}}_ {[0,1,r_1,\ldots ,r_p]} )$, where every automorphism
of the automorphism groups is the composition of elementary maps
\cite{CN}, \cite{CN1}, \cite{N}, \cite{Nam2}, \cite{NC},
\cite{NKW}, \cite{NW}. The results of the paper show that the
${\mathbf F}$-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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참고문헌 (12)
참고문헌 신청
/ / Journal of Applied Algebra and Discrete Structured \it 1 (teson some n-associative algebras}) : 159 ~
/ 1968 / \it An introduction to Lie-admissiblealgebras} : 1225 ~
/ 1969 / \it Groups of Automorphisms of Infinite-Dimensional Simple LieAlgebras} : 707 ~
/ 1974 / \it Description of FilteredLie Algebra with which Graded Lie algebras of Cartan type areAssociated} : 832 ~
/ 1995 / Introduction to nonassociative algebras : 128 ~
/ 1968 / \it An introduction to Lie-admissiblealgebras} : 1225 ~
/ 1969 / \it Groups of Automorphisms of Infinite-Dimensional Simple LieAlgebras} : 707 ~
/ 1974 / \it Description of FilteredLie Algebra with which Graded Lie algebras of Cartan type areAssociated} : 832 ~
/ 1995 / Introduction to nonassociative algebras : 128 ~
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