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Abstract
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 , 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.
Acknowledgments
The authors are grateful to the anonymous referee for careful reading, highly professional working with our manuscript, and valuable suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
Supported by grants AP14870282 of the Ministry of Science and Higher Education of the Republic of Kazakhstan and FAPESP Proc. 2017/21429-6. Supported by grants FAPESP 2018/23690-6, and CNPq 304313/2019-0. Supported by the NNSF of China (Grant No.12101248) and by the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2024A1515013122)