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.
Let (Δ ,σ) be an acyclic quiver Δ with an
admissible automorphism σ such that σ has order pm, 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.