# Representations of Algebras and Related Topics

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#### DOI: 10.4171/101-1/8

Classification problems in noncommutative algebraic geometry and representation theory

Izuru Mori[1]

(1) Shizuoka University, Japan

In noncommutative algebraic geometry, it is interesting to classify homologically nice classes of connected graded algebras. On the other hand, in representation theory of finite dimensional algebras, it is interesting to classify homologically nice classes of finite dimensional algebras. In this survey paper, we will show that there are strong interactions between these classification problems.

Keywords: Artin–Schelter regular algebras, Beilinson algebras, Fano algebras, preprojective algebras, graded Frobenius algebras, trivial extensions