Triangulated Categories in Algebra

The project deals with basic research on triangulated categories in algebra, and partly algebraic topology. The notion of a triangulated category was introduced independently in algebraic geometry by Verdier, based on ideas of Grothendieck, and in algebraic topology by Puppe. These constructions have since played a crucial role in representation theory (derived and stable module categories), algebraic geometry (derived categories of coherent sheaves, theory of motives), commutative algebra, algebraic topology (stable homotopy theory) and other areas of mathematics and theoretical physics.

This is a project dealing with basic research in mathematics. The project deals with various aspects of triangulated categories in algebra and topology. The main research topics in the project are the following: 1. Central ring actions. 2. Cluster cate gories. 3. Dimensions. 4. Higher triangulated structures. A detailed account of these topics is given in the project description.