Nakayama automorphisms of double Ore extensions of Koszul regular algebras
| Autor: | Fred Van Oystaeyen, Yinhuo Zhang, Can Zhu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics::Theory
General Mathematics Ore extension Algebraic geometry Type (model theory) 01 natural sciences Combinatorics Koszul algebra skew polynomial extension double Ore extension skew Laurent extension Nakayama automorphism Calabi-Yau algebra 0103 physical sciences FOS: Mathematics Mathematics::Metric Geometry 0101 mathematics Mathematics Polynomial (hyperelastic model) Algebra homomorphism Mathematics::Commutative Algebra Mathematics::Rings and Algebras 010102 general mathematics Graded ring Mathematics - Rings and Algebras Automorphism Statistics::Computation Number theory Rings and Algebras (math.RA) 16E65 16S36 16U20 010307 mathematical physics |
| Zdroj: | Manuscripta mathematica |
| ISSN: | 0025-2611 |
| Popis: | Let $A$ be a Koszul Artin-Schelter regular algebra and $\sigma$ an algebra homomorphism from $A$ to $M_{2\times 2}(A)$. We compute the Nakayama automorphisms of a trimmed double Ore extension $A_P[y_1, y_2; \sigma]$ (introduced in \cite{ZZ08}). Using a similar method, we also obtain the Nakayama automorphism of a skew polynomial extension $A[t; \theta]$, where $\theta$ is a graded algebra automorphism of $A$. These lead to a characterization of the Calabi-Yau property of $A_P[y_1, y_2; \sigma]$, the skew Laurent extension $A[t^{\pm 1}; \theta]$ and $A[y_1^{\pm 1}, y_2^{\pm 1}; \sigma]$ with $\sigma$ a diagonal type. Comment: The paper has been heavily revised including the title, and will appear in Manuscripta Mathematica |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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