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 modules $𝑆 𝑖, 𝑆 𝑗$ is a semisimple module. #m/def/ralg/hopf The name comes from Chevalley's theorem, which states that for $c h a r 𝕂 = 0$ any group algebra $𝕂 [𝐺]$ has this property.¹

Equivalent characterizations

The Jacobson radical $J a c (𝐻)$ is a Hopf ideal

Proof

#missing/proof

#state/develop | #lang/en | #SemBr

2012. Notes on the Drinfeld double of finite-dimensional group algebras. ↩