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
收藏
页码：4992 / 5004
页数：13
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