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REGULARITY CRITERION AND CLASSIFICATION FOR ALGEBRAS OF JORDAN TYPE

Part of: Rings and algebras with additional structure Algebraic geometry: Foundations Homological methods

Published online by Cambridge University Press:  21 July 2015

Y. SHEN ,
G.-S. ZHOU  and
D.-M. LU
Y. SHEN
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, China e-mail: 11206007@zju.edu.cn; 10906045@zju.edu.cn; dmlu@zju.edu.cn
G.-S. ZHOU
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, China e-mail: 11206007@zju.edu.cn; 10906045@zju.edu.cn; dmlu@zju.edu.cn
D.-M. LU
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, China e-mail: 11206007@zju.edu.cn; 10906045@zju.edu.cn; dmlu@zju.edu.cn
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Abstract

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We show that Artin–Schelter regularity of a $\mathbb{Z}$-graded algebra can be examined by its associated $\mathbb{Z}$r-graded algebra. We prove that there is exactly one class of four-dimensional Artin–Schelter regular algebras with two generators of degree one in the Jordan type. This class is strongly noetherian, Auslander regular, and Cohen–Macaulay. Their automorphisms and point modules are described.

MSC classification

Primary: 16E65: Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
Secondary: 16W50: Graded rings and modules 14A22: Noncommutative algebraic geometry

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 1 , January 2016 , pp. 69 - 95
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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