• Corpus ID: 247218381

Applications of spherical twist functors to Lie algebras associated to root categories of preprojective algebras

@inproceedings{Xu2022ApplicationsOS,
  title={Applications of spherical twist functors to Lie algebras associated to root categories of preprojective algebras},
  author={Fan Xu and Fan Yang},
  year={2022}
}
Let ΛQ be the preprojective algebra of a finite acyclic quiver Q of non-Dynkin type and D(repΛQ) be the bounded derived category of finite dimensional nilpotent ΛQ-modules. We define spherical twist functors over the root category RΛQ of D (repΛQ) and then realize the Weyl group associated to Q as certain subquotient of the automorphism group of the Ringel-Hall Lie algebra g(RΛQ) of RΛQ induced by spherical twist functors. We also present a conjectural relation between certain Lie subalgebras… 

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