Skip to main content
MathOverflow

Return to Question

deleted 2 characters in body; edited title
Source Link
Konstantinos Kanakoglou
Konstantinos Kanakoglou
  • 7.7k
  • 2
  • 23
  • 64

Extending an elements of the dual of a Hopf subalgebra to the Hopf dual of the whole algebra

I have a question about Hopf duals. To begin we can remind the definition: For an Hopf algebra $A$ over a field $k$, the Hopf dual $A^{\circ}$ is the subspace of the linear dual $\mathrm{Lin}_k(A,k)$ consisting of elements that vanish on some two-sided ideal $I \subseteq A$ withof finite codimension (i.e. $\mathrm{dim}(A/I) < \infty$).

Let $B$ be a Hopf subalgebra of $A$. We can certainly consider the Hopf dual $B^{\circ}$. Is it true that any element of $B^{\circ}$ can be extended to an element of $A^{\circ}$?

Extending an elements of a Hopf subalgebra to the Hopf dual of the whole algebra

I have a question about Hopf duals. To begin we can remind the definition: For an Hopf algebra $A$ over a field $k$, the Hopf dual $A^{\circ}$ is the subspace of the linear dual $\mathrm{Lin}_k(A,k)$ consisting of elements that vanish on some two-sided ideal $I \subseteq A$ with finite codimension (i.e. $\mathrm{dim}(A/I) < \infty$).

Let $B$ be a Hopf subalgebra of $A$. We can certainly consider the Hopf dual $B^{\circ}$. Is it true that any element of $B^{\circ}$ can be extended to an element of $A^{\circ}$?

Extending elements of the dual of a Hopf subalgebra to the Hopf dual of the whole algebra

I have a question about Hopf duals. To begin we can remind the definition: For an Hopf algebra $A$ over a field $k$, the Hopf dual $A^{\circ}$ is the subspace of the linear dual $\mathrm{Lin}_k(A,k)$ consisting of elements that vanish on some two-sided ideal $I \subseteq A$ of finite codimension (i.e. $\mathrm{dim}(A/I) < \infty$).

Let $B$ be a Hopf subalgebra of $A$. We can certainly consider the Hopf dual $B^{\circ}$. Is it true that any element of $B^{\circ}$ can be extended to an element of $A^{\circ}$?

Source Link
Alain Rochefort
Alain Rochefort
  • 305
  • 1
  • 3

Extending an elements of a Hopf subalgebra to the Hopf dual of the whole algebra

I have a question about Hopf duals. To begin we can remind the definition: For an Hopf algebra $A$ over a field $k$, the Hopf dual $A^{\circ}$ is the subspace of the linear dual $\mathrm{Lin}_k(A,k)$ consisting of elements that vanish on some two-sided ideal $I \subseteq A$ with finite codimension (i.e. $\mathrm{dim}(A/I) < \infty$).

Let $B$ be a Hopf subalgebra of $A$. We can certainly consider the Hopf dual $B^{\circ}$. Is it true that any element of $B^{\circ}$ can be extended to an element of $A^{\circ}$?