Representation Theory and Mathematical Physics Seminar: Supports and tensor ideals in stable module categories.
Seminar | September 20 | 4-5 p.m. | 939 Evans Hall
Julia Pevtsova, University of Washington
Classifying modules up to direct sums in modular representation theory is usually a hopeless task – there are too many indecomposable modules (over a field of characteristic $p$) even for such a seemingly small group as $Z/3 \times Z/3$ or a three dimensional Heisenberg Lie algebra. Inspired by ideas from stable homotopy theory and algebraic geometry we suggest a different way of organizing our understanding of modular representations. Namely, we seek to classify modules up to homological operations: not only direct sums, but also extensions, syzygies and tensor products with simple modules. I will describe both the problem and the answer which involves cohomology and support varieties. Based on joint work with D. Benson, S. Iyengar, H. Krause.