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G-Groups of Cohen-Macaulay Rings with n-Cluster Tilting Objects

  • Zachary FloresEmail author
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Abstract

Let \((R, \mathfrak {m}, k)\) denote a local Cohen-Macaulay ring such that the category of maximal Cohen-Macaulay R-modules mcmR contains an n-cluster tilting object L. In this paper, we compute the Quillen K-group G1(R) := K1(modR) explicitly as a direct sum of a finitely generated free abelian group and an explicit quotient of AutR(L)ab when R is a k-algebra and k is algebraically closed with characteristic not two. Moreover, we compute AutR(L)ab and G1(R) for certain hypersurface singularities.

Keywords

Cohen-Macaulay n-cluster tilting K-theory Hypersurface singularities Automorphism groups 

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Notes

Acknowledgments

The author would like to thank Hailong Dao and Jeanne Duflot for their useful comments in the preparation of this manuscript. We would also like to thank the anonymous referee for greatly improving the quality of this manuscript.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsFort CollinsUSA

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