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 *k*Δ⊗_{k}*kG*, 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.