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An exceptional cycle in a triangulated category with Serre functor is ageneralization of a spherical object. Suppose that $A$ and $B$ are Gorensteinalgebras, given a perfect exceptional $n$-cycle $E_*$ in $K^b(A\mbox{-}{\rmproj})$ and a perfect exceptional $m$-cycle $F_*$ in $K^b(B\mbox{-}{\rmproj})$, we construct an $A$-$B$-bimodule $N$, and prove the product$E_*\boxtimes F_*$ is an exceptional $(n+m-1)$-cycle in$K^b(\Lambda\mbox{-}{\rm proj})$, where $\Lambda=\begin{pmatrix}A & N\\ 0 & B\end{pmatrix}$. Using this construction, one gets many new exceptional cycleswhich is unknown before for certain class of algebras.

Exceptional cycles in triangular matrix algebras