The Picard group Tk(G) of the stable module category of a finite group has been an important object of study in modular representation theory, starting with work Dade in the 1970s. Its elements are equivalence classes of so-called endotrivial modules, i.e., modules M such that End(M) is isomorphic to a trivial module direct sum a projective kG-module. 1-dimensional characters, and their shifts, are examples of such modules, but often exotic elements exist as well. My talk will be a guided tour of how to calculate Tk(G), using methods from homotopy theory. The tour will visit joint work with Tobias Barthel and Joshua Hunt, with Jon Carlson, Nadia Mazza and Dan Nakano, and with Achim Krause.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
