All Questions

Let $A$ be a Hopf algebra (over a field). Consider a unital subalgebra $B\subseteq A$ with $\Delta(B)\subseteq B\otimes A$. Put $$B^+:= B\cap \ker(\epsilon).$$ It can be shown that $B^+$ is a two-...

A coalgebra is a triple $(A,\Delta,\epsilon)$ consisting of a vector space, a coproduct, and a counit. Now as we all know, just like the unit in an algebra, the counit of a coalgebra is unique, i.e. ...

Is it possible to classify Hopf algebras $H$, over a field $k$, which admit a unique (up to isomorphism) irreducible comodule, namely the trivial $1$-dim comodule $$ k \to k \otimes H, ~~ k \mapsto k ...

A cosemisimple Hopf algebra is usually defined to a Hopf algebra which is the sum of its cosimple subcoalgebras. Does this definition assume that each cosimple subcoalgebra appears only once in the ...