Some algebras that are not silting connected

Silting and Tilting for Weakly Symmetric Algebras

“…One can contrast these relations with those of the untwisted trivial extension, which are described just after Question 1 in [11]. Furthermore, while the Nakayama automorphism of the untwisted trivial extension is the identity, we can see from Eq.…”

“…not necessarily irreducible) mutations, left or right at each stage. Note that not all algebras are weakly siltingconnected [11].…”

“…We now give examples of weakly symmetric algebras with silting complexes that are not tilting. The examples are based on those in [11], so we begin by reviewing the necessary details from that work.…”

“…(4.C) that the Nakayama automorphism on swaps each pair x and y (of parallel arrows), while also swapping u and v. For n = 4, the tilting complex T ∈ K b (proj A) from Eq. (4.A) is described in [11]. The corresponding complex T ⊗ A ∈ K b (proj ) will look the same, but with each A replaced by .…”