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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

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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

Information

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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