Free commutative two-step-associative algebras

被引：0

作者：

Ismailov, Nurlan ^{[1
]}

Shestakov, Ivan ^{[2
,3
]}

Zhang, Zerui ^{[4
]}

机构：

[1] Astana IT Univ, Astana, Kazakhstan

[2] Univ Sao Paulo, Inst Matemat & Stat, Sao Paulo, Brazil

[3] Sobolev Inst Math, Novosibirsk, Russia

[4] South China Normal Univ, Sch Math Sci, Guangzhou, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2024年 / 52卷 / 12期

基金：

巴西圣保罗研究基金会;

关键词：

Automorphism; commutative two-step-associative algebra; Jacobian matrix; AUTOMORPHISMS; RINGS;

D O I：

10.1080/00927872.2024.2362345

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct linear bases for free commutative two-step-associative algebras and study their automorphisms. It turns out that every automorphism of a polynomial algebra without unit can be lifted to an automorphism of a free commutative two-step-associative algebra. Moreover, for any n >= 2, a wild automorphism is constructed for the n-generated free commutative two-step-associative algebra which is not stably tame and cannot be lifted to an automorphism of the n-generated free commutative nonassociative algebra.

引用

页码：4992 / 5004

页数：13

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