Higher Auslander Algebras and Higher Representation Finite Algebras

Explore the concept of Higher Auslander algebras in this 48-minute conference talk from the Canada-Mexico-US Conference on Representation Theory, Noncommutative Algebra, and Categorification. Delve into Maurice Auslander's celebrated theorem on artin algebras, which establishes a correspondence between algebras of finite representation type and Auslander algebras. Learn about O. Iyama's introduction of Higher Auslander algebras and their relationship to higher representation finite algebras. Discover recent work by Emre Sen on constructing new families of Higher Auslander algebras and the resulting higher representation finite algebras. Examine a joint paper by the speaker, Emre Sen, and Shijie Zhu, presenting an alternative method for constructing Higher Auslander algebras within Nakayama algebras. Gain insights into the ongoing challenges in understanding Higher Auslander algebras, higher representation finite algebras, and higher cluster tilting modules, emphasizing the importance of creating new families to advance the field.