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<p>Given an action of a finite group on a triangulated category with a suitable strong exceptional collection, a construction of Elagin produces an associated strong exceptional collection on the equivariant category. In the untwisted case, we prove that the endomorphism algebra of the induced exceptional collection is the basic reduction of the skew group algebra of the endomorphism algebra of the original exceptional collection.</p>

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Endomorphism Algebras of Equivariant Exceptional Collections

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月7日

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  • Andreas Krug,
  • Erik Nikolov

摘要

Given an action of a finite group on a triangulated category with a suitable strong exceptional collection, a construction of Elagin produces an associated strong exceptional collection on the equivariant category. In the untwisted case, we prove that the endomorphism algebra of the induced exceptional collection is the basic reduction of the skew group algebra of the endomorphism algebra of the original exceptional collection.