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Mathematics, Representation Theory
Abstract:
If A is a finite-dimensional symmetric algebra, then it is well-known that
the only silting complexes in $\mathrm{K^b}(\mathrm{proj}A)$ 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.
