Tuesday, July 24, 14:00, 7.527

Raphael Bennett-Tennenhaus (Bielefeld), Semilinear clannish algebras with idempotent loops.

Abstract:
Clannish algebras are quotients of path algebras introduced by Crawley-Boevey. Each relation is either a path, or a quadratic polynomial in a loop. Allowing semilinear maps between vector spaces, a theorem of Kottwitz-Rapoport is recovered from a module classification. Representations arising in work of Geuenich-Labardini-Fragoso are given by permitting irreducible quadratics. Other examples are found in work of Dlab-Ringel and work of Klingler-Levy. In joint work with Crawley-Boevey (plms.12637), we gave a module classification, assuming the quadratics have non-zero constant terms. I will talk about ongoing work that continues this project, where we also allow constant terms to be 0, and explain the new modules that arise.