Abstract
In this expository note, I present some of the key features of the lattice of torsion classes of a finite-dimensional algebra, focussing in particular on its complete semidistributivity and consequences thereof. This is intended to serve as an introduction to recent work by Barnard–Carroll–Zhu and Demonet–Iyama–Reading–Reiten–Thomas.
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Acknowledgements
I would like to thank my coauthors on [7, 11, 15], from whom I have learned a great deal. It is my pleasure to acknowledge NSERC and the Canada Research Chairs program for their financial support. Thanks to Nathan Reading, Alexander Garver, and two anonymous referees for helpful comments on this manuscript. I am extremely grateful to have been given the opportunity to present this material at Zhejiang University in 2018 and at the Isfahan School on Representations of Algebras in 2019. Thanks to Fang Li for the invitation to Zhejiang and to the organizers of the Isfahan School and Conference on Representations of Algebras, and in particular Javad Asadollahi, for the invitation to speak in Isfahan, and for the invitation to prepare this contribution to the special issue.
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Communicated by Javad Asadollahi.
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Thomas, H. An Introduction to the Lattice of Torsion Classes. Bull. Iran. Math. Soc. 47 (Suppl 1), 35–55 (2021). https://doi.org/10.1007/s41980-021-00545-3
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DOI: https://doi.org/10.1007/s41980-021-00545-3