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

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 $kP$ of $p$-groups in characteristic $p$, we recover all the stable auto-equivalences corresponding to endo-trivial modules over $kP$ 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.