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GRADED MORITA EQUIVALENCES FOR GEOMETRIC AS-REGULAR ALGEBRAS

Published online by Cambridge University Press:  02 August 2012

IZURU MORI
Affiliation:
Department of Mathematics, Faculty of Science, Shizuoka University, Shizuoka 422-8529, Japan e-mail: simouri@ipc.shizuoka.ac.jp
KENTA UEYAMA
Affiliation:
Department of Information Science and Technology, Graduate School of Science and Technology, Shizuoka University, Shizuoka 422-8529, Japan e-mail: f5144004@ipc.shizuoka.ac.jp
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Abstract

Classification of AS-regular algebras is one of the major projects in non-commutative algebraic geometry. In this paper, we will study when given AS-regular algebras are graded Morita equivalent. In particular, for every geometric AS-regular algebra A, we define another graded algebra A, and show that if two geometric AS-regular algebras A and A' are graded Morita equivalent, then A and A' are isomorphic as graded algebras. We also show that the converse holds in many three-dimensional cases. As applications, we apply our results to Frobenius Koszul algebras and Beilinson algebras.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

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