[[Hopf theory MOC]]
# Chevalley property

A [[K-bimonoid]] $H$ is said to have the **Chevalley property** iff the tensor product $S_{i} \otimes S_{j}$ of any two [[simple module|simple modules]] $S_{i},S_{j}$ is a [[semisimple module]]. #m/def/falg/hopf
The name comes from [[Chevalley's theorem]], which states that for [[Characteristic|$\opn{char}\mathbb K = 0$]] any [[Group ring|group algebra]] $\mathbb{K}[G]$ has this property.[^2012]

  [^2012]: 2012\. [[Sources/@chenNotesDrinfeldDouble2012|Notes on the Drinfeld double of finite-dimensional group algebras]].

## Equivalent characterizations

- The [[Jacobson radical]] $J(H)$ is a [[Hopf ideal]]

> [!missing]- Proof
> #missing/proof

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