Silting and Tilting for Weakly Symmetric Algebras

DOI10.1007/S10468-021-10090-6arXiv2101.03097MaRDI QIDQ6357857

Alex S. Dugas, Jenny August

Publication date: 8 January 2021

Abstract: If A is a finite-dimensional symmetric algebra, then it is well-known that the only silting complexes in $mathrm{K}^b(mathrmprojA)$ are the tilting complexes. In this note we investigate to what extent the same can be said for weakly symmetric algebras. On one hand, we show that this holds for all tilting-discrete weakly symmetric algebras. In particular, a tilting-discrete weakly symmetric algebra is also silting-discrete. On the other hand, we also construct an example of a weakly symmetric algebra with silting complexes that are not tilting.

Mathematics Subject Classification ID

Representations of associative Artinian rings (16G10) Derived categories, triangulated categories (18G80)

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