An introduction to relative Calabi-Yau structures
Abstract
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.
Cite
@article{arxiv.2111.10771,
title = {An introduction to relative Calabi-Yau structures},
author = {Bernhard Keller and Yu Wang},
journal= {arXiv preprint arXiv:2111.10771},
year = {2023}
}
Comments
17 pages; v2: Added reminder on cyclic homology, corrected typos, to appear in the proceedings of the ICRA 2020 (online); v3: References corrected and updated