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

Nengqun Li; Yuming Liu

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arXiv · 2310.13934

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

Nengqun Li·Yuming Liu

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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.

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BibTeX RIS

Nengqun Li, Yuming Liu. 2023-10-21. A generalization of Dugas' construction on stable auto-equivalences for symmetric algebras. https://arxiv.org/abs/2310.13934

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