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.
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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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Presented by: Michel Van den Bergh
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Flores, Z. G-Groups of Cohen-Macaulay Rings with n-Cluster Tilting Objects. Algebr Represent Theor 23, 887–916 (2020). https://doi.org/10.1007/s10468-019-09876-6
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DOI: https://doi.org/10.1007/s10468-019-09876-6