NAKAYAMA AUTOMORPHISMS OF ORE EXTENSIONS OVER POLYNOMIAL ALGEBRAS

Abstract

Abstract 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 E G is also investigated in terms of Zhang’s twist, where G is a cyclic group sharing the same order with σ .