# AUTOMORPHISMS OF A WEYL-TYPE ALGEBRA I

Choi, Seul-Hee

• Published : 2006.01.01
• 51 2

#### Abstract

Every non-associative algebra L corresponds to its symmetric semi-Lie algebra $L_{[,]}$ with respect to its commutator. It is an interesting problem whether the equality $Aut{non}(L)=Aut_{semi-Lie}(L)$ holds or not [2], [13]. We find the non-associative algebra automorphism groups $Aut_{non}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ and $Aut_{non-Lie}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ 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.┌ᘀ؀䡏䡈䉚ᔀ胭閜鳬鶘駭验耀

#### Keywords

simple;non-associative algebra;semi-Lie algebra;automorphism;locally identity;annihilator;Jacobian conjecture;self-centralizing

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