Nakayama automorphisms play an important role in the fields of noncommutative algebraic geometry and noncommutative invariant theory. However, their computations are not easy in general. We compute the Nakayama automorphism ν of an Ore extension R[x; σ, δ] over a polynomial algebra R in n variables for an arbitrary n. The formula of ν is obtained explicitly. When σ is not the identity map, the invariant EG is also investigated in terms of Zhang’s twist, where G is a cyclic group sharing the same order with σ.

中文翻译：

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多项式代数上矿石扩展的中山自同态

中山自同构在非交换代数几何和非交换不变量理论领域发挥着重要作用。但是，它们的计算通常并不容易。我们计算 Nakayama 自同构ν矿石延伸R[X; σ, δ] 在多项式代数上R在n任意变量n. 的公式ν是明确获得的。什么时候σ不是恒等映射，不变量乙G还根据张的扭曲进行了调查，其中G是一个循环群，与σ.