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arXiv · 2512.24357

On $R$-equivalence of Automorphism Groups of Associative Algebras

Dibyendu Das
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Abstract

Let $A$ be a finite-dimensional associative $k$-algebra with identity. The primary aim of this paper is to study the rationality properties of the group of all $k$-algebra automorphisms of $A$, as an affine algebraic group over an arbitrary field $k$. We investigate mainly the $R$-equivalence property of the identity component of $\mathrm{Aut}_{k}(A)$ over a perfect field $k$.

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Dibyendu Das. 2025-12-30. On $R$-equivalence of Automorphism Groups of Associative Algebras. https://arxiv.org/abs/2512.24357

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