AUTOMORPHISMS OF A WEYL-TYPE ALGEBRA I

Title & Authors
AUTOMORPHISMS OF A WEYL-TYPE ALGEBRA I
Choi, Seul-Hee;

Abstract
Every non-associative algebra L corresponds to its symmetric semi-Lie algebra $\small{L_{[,]}}$ with respect to its commutator. It is an interesting problem whether the equality $\small{Aut{non}(L)=Aut_{semi-Lie}(L)}$ holds or not [2], [13]. We find the non-associative algebra automorphism groups $\small{Aut_{non}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}}$ and $\small{Aut_{non-Lie}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}}$ 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;
Language
English
Cited by
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