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An introduction to relative Calabi-Yau structures
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An introduction to relative Calabi-Yau structures
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These are notes taken by the second author for a series of three lectures by the first author on absolute and relative Calabi-Yau completions and Calabi-Yau structures given at the workshop of the International Conference on Representations of Algebras which was held online in November 2020. Such structures are relevant for (higher) representation theory as well as for the categorification of cluster algebras with coefficients. After a quick reminder on dg categories and their Hochschild and cyclic homologies, we present examples of absolute and relative Calabi-Yau completions (in the sense of Yeung). In many examples, these are related to higher preprojective algebras in the sense of Iyama-Oppermann. We conclude with the definition of relative (left and right) Calabi-Yau structures after Brav-Dyckerhoff.
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Cited by 1 Pith paper
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The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures
The Auslander-Iyama correspondence is extended to bimodule right Calabi-Yau dg algebras via a new Massey bimodule cohomology, with an obstruction (BV operator on universal Massey product) and a first non-liftable example.
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