报告题目：n-translation algebras, n-Fano algebras and higher representation theory
摘要：Start with a stable n-translation algebra, we study the $\tau$-slice algebra and dual $\tau$-slice algebras. Such algebras, especially dual $\tau$-slice algebras, are closed related to Iyama's higher representation theory. We show that $n$-APR tilts of such algebra are characterized by $\tau$-mutation, the Auslander of $\tau_n$ closure and $\nu_n$-closure are characterised by the $\mathbb Z|n Q$ construction introduced for constructing $n$-translation algebras. In the Koszul case, such dual $\tau$-slice algebras are $(n-1)$-Fano algebras introduced by Minamoto. Using $n$-translation algebra, we give a construction of a sequence of $n+t$-Fano algbras when an $n$-Fano algebra is given. We also show that for such $(n-1)$-Fano algebra, preprojective algebras and the twisted trivial extension of its quadratic dual are related by quadratic dual.