A generalization of Dugas' construction on stable auto-equivalences for symmetric algebras

Nengqun Li; Yuming Liu

paper

A generalization of Dugas' construction on stable auto-equivalences for symmetric algebras

arXiv:2310.13934

Abstract

We give a unified generalization of Dugas' construction on stable auto-equivalences of Morita type from local symmetric algebras to arbitrary symmetric algebras. For group algebras $k P$ of $p$ -groups in characteristic $p$ , we recover all the stable auto-equivalences corresponding to endo-trivial modules over $k P$ except that $P$ is generalized quaternion of order $2^{m}$ . Moreover, we give many examples of stable auto-equivalences of Morita type for non-local symmetric algebras.