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arXiv · 2211.10781

Automorphisms and derivations of affine commutative and PI-algebras

Oksana Bezushchak·Anatoliy Petravchuk·Efim Zelmanov
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Abstract

We prove analogs of A.~Selberg's result for finitely generated subgroups of $\text{Aut}(A)$ and of Engel's theorem for subalgebras of $\text{Der}(A)$ for a finitely generated associative commutative algebra $A$ over an associative commutative ring. We prove also an analog of the theorem of W.~Burnside and I.~Schur about locally finiteness of torsion subgroups of $\text{Aut}(A)$.

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Oksana Bezushchak, Anatoliy Petravchuk, Efim Zelmanov. 2022-11-19. Automorphisms and derivations of affine commutative and PI-algebras. https://arxiv.org/abs/2211.10781

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