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Andrea Pena
Andrea Pena
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Background:

Let $H$ be a finitely generated commutative Hopf $k$-algebra, where $k$ is a field of non-zero characteristic. For $$ \widehat{H} := \text{Alg}_k\{H; k\}, $$ we recall (see Abe Chapter 4 for example) that the Hopf algebra structure of $H$ induces in a canonical way a group structure on $\widehat{H}$.

QuastionQuestion:

Is it true that the category of finite-dimensional modules over $\widehat{H}$ is equivalent to the category of finite-dimensional co-modules over $H$. If so, what is a good reference for this?

Background:

Let $H$ be a finitely generated commutative Hopf $k$-algebra, where $k$ is a field of non-zero characteristic. For $$ \widehat{H} := \text{Alg}_k\{H; k\}, $$ we recall (see Abe Chapter 4 for example) that the Hopf algebra structure of $H$ induces in a canonical way a group structure on $\widehat{H}$.

Quastion:

Is it true that the category of finite-dimensional modules over $\widehat{H}$ is equivalent to the category of finite-dimensional co-modules over $H$. If so, what is a good reference for this?

Background:

Let $H$ be a finitely generated commutative Hopf $k$-algebra, where $k$ is a field of non-zero characteristic. For $$ \widehat{H} := \text{Alg}_k\{H; k\}, $$ we recall (see Abe Chapter 4 for example) that the Hopf algebra structure of $H$ induces in a canonical way a group structure on $\widehat{H}$.

Question:

Is it true that the category of finite-dimensional modules over $\widehat{H}$ is equivalent to the category of finite-dimensional co-modules over $H$. If so, what is a good reference for this?

deleted 2 characters in body
Source Link
Andrea Pena
Andrea Pena
  • 401
  • 2
  • 10

Background:

Let $H$ be a finitely generated commutative Hopf $k$-algebra, where $k$ is a field of non-zero characteristic. For $$ \widehat{H} := \text{Lin}_k\{H; k\}, $$$$ \widehat{H} := \text{Alg}_k\{H; k\}, $$ we recall (see Abe Chapter 4 for example) that the Hopf algebra structure of $H$ induces in a canonical way a group structure on $\widehat{H}$.

Quastion:

Is it true that the category of finite-dimensional modules over $\widehat{H}$ is equivalent to the category of finite-dimensional co-modules over $H$. If so, what is a good reference for this?

Background:

Let $H$ be a finitely generated commutative Hopf $k$-algebra, where $k$ is a field of non-zero characteristic. For $$ \widehat{H} := \text{Lin}_k\{H; k\}, $$ we recall (see Abe Chapter 4 for example) that the Hopf algebra structure of $H$ induces in a canonical way a group structure on $\widehat{H}$.

Quastion:

Is it true that the category of finite-dimensional modules over $\widehat{H}$ is equivalent to the category of finite-dimensional co-modules over $H$. If so, what is a good reference for this?

Background:

Let $H$ be a finitely generated commutative Hopf $k$-algebra, where $k$ is a field of non-zero characteristic. For $$ \widehat{H} := \text{Alg}_k\{H; k\}, $$ we recall (see Abe Chapter 4 for example) that the Hopf algebra structure of $H$ induces in a canonical way a group structure on $\widehat{H}$.

Quastion:

Is it true that the category of finite-dimensional modules over $\widehat{H}$ is equivalent to the category of finite-dimensional co-modules over $H$. If so, what is a good reference for this?

Source Link
Andrea Pena
Andrea Pena
  • 401
  • 2
  • 10

Algebraic Groups, Modules, and Comodules

Background:

Let $H$ be a finitely generated commutative Hopf $k$-algebra, where $k$ is a field of non-zero characteristic. For $$ \widehat{H} := \text{Lin}_k\{H; k\}, $$ we recall (see Abe Chapter 4 for example) that the Hopf algebra structure of $H$ induces in a canonical way a group structure on $\widehat{H}$.

Quastion:

Is it true that the category of finite-dimensional modules over $\widehat{H}$ is equivalent to the category of finite-dimensional co-modules over $H$. If so, what is a good reference for this?