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NAKAYAMA AUTOMORPHISMS OF ORE EXTENSIONS OVER POLYNOMIAL ALGEBRAS

Part of: Homological methods Rings and algebras with additional structure Rings and algebras arising under various constructions

Published online by Cambridge University Press:  17 June 2019

LIYU LIU Open the ORCID record for LIYU LIU [Opens in a new window]  and
WEN MA
LIYU LIU
Affiliation:
School of Mathematical Sciences, Yangzhou University, No. 180 Siwangting Road, 225002 Yangzhou, Jiangsu, China e-mail: lyliu@yzu.edu.cn; 2922117517@qq.com
WEN MA
Affiliation:
School of Mathematical Sciences, Yangzhou University, No. 180 Siwangting Road, 225002 Yangzhou, Jiangsu, China e-mail: lyliu@yzu.edu.cn; 2922117517@qq.com
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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 EG is also investigated in terms of Zhang’s twist, where G is a cyclic group sharing the same order with σ.

MSC classification

Primary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
Secondary: 16S36: Ordinary and skew polynomial rings and semigroup rings 16W22: Actions of groups and semigroups; invariant theory
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 3 , September 2020 , pp. 518 - 530
Copyright
© Glasgow Mathematical Journal Trust 2019

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