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Automorphisms of finitely generated relatively free bicommutative algebras
Journal of Pure and Applied Algebra ( IF 0.8 ) Pub Date : 2021-08-01 , DOI: 10.1016/j.jpaa.2020.106636
Ivan Shestakov , Zerui Zhang

Abstract Automorphisms of free bicommutative algebras over an arbitrary field are studied. Wild automorphisms are constructed in two-generated and three-generated free bicommutative algebras. Moreover, for any n ≥ 2 , a wild automorphism is constructed in the n-generated free associative bicommutative algebra which is not stably tame and can not be lifted to an automorphism of the n-generated free bicommutative algebra.

中文翻译:

有限生成的相对自由双对易代数的自同构

摘要 研究了任意域上自由双对易代数的自同构。野生自同构是在二生成和三生成的自由双交换代数中构建的。此外,对于任何 n ≥ 2 ,在 n 生成的自由关联双对易代数中构造了一个野生自同构,它不是稳定驯服的,不能提升到 n 生成的自由双对易代数的自同构。
更新日期:2021-08-01
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