Quiver representations, singularity categories, and monoidal structures

点击翻译按钮获取中文摘要

Representations of algebras are studied from various directions, involving monoidal and triangulated structures. One goal is to describe in terms of generators and relations representation rings and monoids of projections functors for representations of quivers. Another goal is to classify thick and localising subcategories of triangulated singularity categories. This involves continuous and discrete parametrisations, reflecting the existing monoidal or combinatorial structures. The choice of singularity categories is motivated by connections with the representation theory of finite groups, the study of matrix factorisations, and applications in algebraic geometry, including weighted projective lines.