Abstract
We describe the group G = AutEnd(K[x 1 , . . . , x n ]), where K is an arbitrary field. A similar result is obtained also for the automorphism group of the category \( \mathcal{C}{\mathcal{A}^{\circ }} \) of finitely generated free commutative-associative algebras of the variety commutative algebras. This solves two problems posed by B. Plotkin ( [4, Problems 12 and 15]).
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References
A. Berzins, “The group of automorphisms of the semigroup of endomorphisms of free commutative and free associative algebras,” Int. J. Algebra Comput., 17, Nos. 5-6, 941–949 (2007).
A. Belov-Kanel, A. Berzins, and R. Lipyanski, “Automorphisms of the endomorphism semigroup of a free associative algebra,” Int. J. Algebra Comput., 17, Nos. 5-6, 923–939 (2007).
B. Lipyanski, “Automorphisms of the endomorphism semigroups of free linear algebras of homogeneous varieties,” Lin. Algebra Appl., 429, No. 1, 156–180 (2008).
B. Plotkin, “Algebras with the same (algebraic) geometry,” Tr. Mat. Inst. Steklova, 242, 176–207 (2003).
B. Plotkin and G. Zhitomirski, “Automorphisms of categories of free algebras of some varieties,” J. Algebra, 306, No. 2, 344–367 (2006).
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 74, Proceedings of the International Conference “Modern Algebra and Its Applications” (Batumi, 2010), Part 1, 2011.
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Belov-Kanel, A., Lipyanski, R. Automorphisms of the semigroup End(K[x 1 , . . . , x n ]). J Math Sci 186, 706–711 (2012). https://doi.org/10.1007/s10958-012-1018-6
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DOI: https://doi.org/10.1007/s10958-012-1018-6