Exceptional cycles in triangular matrix algebras.

An exceptional cycle in a triangulated category with Serre functor is a generalization of a spherical object. Suppose that A and B are Gorenstein algebras, given a perfect exceptional n -cycle E ⁎ in K b (A - proj) and a perfect exceptional m -cycle F ⁎ in K b (B - proj) , we construct an A - B -bimodule N , and prove the product E ⁎ ⊠ F ⁎ is an exceptional (n + m − 1) -cycle in K b (Λ - proj) , where Λ = ( A N 0 B ). Using this construction, one gets many new exceptional cycles which is unknown before for certain class of algebras. [ABSTRACT FROM AUTHOR]