Tuesday, October 15, 14:00, 7.527

Ren Wang (University of Science and Technology of China, Hefei), Skew group algebras and algebras associated to Cartan matrices.

Abstract:
Let (Δ ,σ) be an acyclic quiver Δ with an admissible automorphism σ such that σ has order p^m, where p is a prime number and m>0. Let k be a field with characteristic p. We prove that the skew group algebra kΔ⊗_kkG, where G is the cyclic group generated by σ, is Morita equivalent to an algebra defined in [C. Geiss, B. Leclerc, and J. Schröer, Quivers with relations for symmetrizable Cartan matrices I: Foundations, Invent. Math. 209 (2017), 61-158], which is associated to a symmetrizable Cartan matrix. In this case, we prove that τ-locally free modules of the skew group algebra are exactly indecomposable induced modules. This is ongoing joint work with Xiao-Wu Chen.