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<p>We show that two finite-dimensional Hopf algebras are gauge equivalent if and only if their bounded derived categories are monoidal triangulated equivalent. More generally, a monoidal derived equivalence between locally finite tensor Grothendieck categories induces a monoidal abelian equivalence.</p>

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Hopf algebras are determined by their monoidal derived categories

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Yuying Xu,
  • Junhua Zheng

摘要

We show that two finite-dimensional Hopf algebras are gauge equivalent if and only if their bounded derived categories are monoidal triangulated equivalent. More generally, a monoidal derived equivalence between locally finite tensor Grothendieck categories induces a monoidal abelian equivalence.