Algebra and Number Theory Seminar Spring 2017
April 7, 2017
April 14, 2017
Rob Carman, UCSC
April 21, 2017
Markus Linckelmann, City University, London
Title: On Triangulated Categories in Representation Theory
Abstract: There are two types of triangulated categories which arise routinely in modular representation theory - derived categories, and stable module categories.
Derived categories determine many fundamental numerical invariants of algebras, such as the number of isomorphism classes of simple modules and irreducible characters.
By contrast, it is not known whether stable module categories determine any of the above mentioned numerical invariants in general. This is one of the major obstacles in modular representation theory. Unlike derived categories, stable module categories need not have any t-structures, and hence their stability spaces in the sense of Bridgeland may be empty. Still, a stable module category may have many abelian subcategories whose exact structure is compatible with the triangulated structure, and whose numerical invariants are, in some cases, those of the original algebra. We will describe a simple construction principle for abelian subcategories of stable module categories.
April 28, 2017
May 5, 2017
May 12, 2017
May 19, 2017
May 26, 2017
June 2, 2017
June 9, 2017
June 16, 2017