On the relation between cluster and classical tilting |
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| Authors: | Thorsten Holm,Peter Jø rgensen |
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| Affiliation: | a Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Fakultät für Mathematik und Physik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
b School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom |
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| Abstract: | Let  be a triangulated category with a cluster tilting subcategory U. The quotient category  is abelian; suppose that it has finite global dimension.We show that projection from  to  sends cluster tilting subcategories of  to support tilting subcategories of  , and that, in turn, support tilting subcategories of  can be lifted uniquely to weak cluster tilting subcategories of  . |
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| Keywords: | 16G70 18E10 18E30 18G99 |
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