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Title:
Matrix Factorizations and Tilting Objects
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Abstract:
Whenever a triangulated category admits a tilting object T, it identifies with the derived category of E = End(T). How does one get back from that derived category to the original one? We describe an algorithm for the case that E is an artinian algebra of finite global dimension. As an example, we use this to identify all matrix factorizations of y^d - x^d for d ≥ 2, thus, answering a question raised several years ago by physicists. We will aa well discuss the case of cubic hepersurfaces, where some intriguing representation theoretic problems occur.
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