All Questions
Tagged with hopf-algebras comodules
10
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Exercise 3.14b of Waterhouse Affine Group Schemes
I have been working on Exercise 3.14b of Waterhouse Introduction to Affine Group Schemes and want to make sure I am on the right track.
Suppose G is represented by A. Write down the map $\varphi: A \...
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Change of scalars for comodules as adjunctions?
Let $k$ be a commutative ring and $f: C \to C'$ be a homomorphism of $k$-coalgebras (for simplicity, we can suppose that it is surjective so that $f(C) = C'$). There is a functor:
$$f_*: {}^lC-comod \...
- 493
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Regular functions on torsors
Let $X \rightarrow Y$ be a torsor for a linear algebraic group $G$ (i.e. $X$ is a principal $G$-bundle over $Y$). Assume also that both $X$, and $Y$ are affine. What can be said about $\mathbb{C}[X]$ ...
- 135
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How exactly does the coaction on the comodule X*⊗X work?
I'm struggling a bit with Sweedler notation. Let $(H,∆,ε,S,m,u)$ be a Hopf algebra over a commutative ring $k$ and let $X,Y$ be right $H$-comodules which are finitely generated projective as $k$-...
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$H$-comodule structure of $A\otimes_K A$
I'm studying the paper "Hopf Galois Theory: A survey" by Susan Montgomery, and need some help with something that the paper does not define (and that I'm not able to find anywere). Consider ...
- 3,564
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Prove $A$ is $K[G]$-comodule algebra
I'm studying the paper "Hopf Galois Theory: A survey" by Susan Montgomery, and there's something I'm trying to prove for what I may need some help.
More precisely, is this statement from ...
- 3,564
2
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Isomorphism between two Hopf algebras
Let $k$ be a field, over which we consider algebras and coalgebras. A $k$-coalgebra is a comonoid object in $k$-modules, and a $k$-algebra is a monoid object in $k$-modules. A $k$-bialgebra is ...
user900250
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The kernel of a morphism of co-rings is a co-ideal
I would like to show that
The Kernel of a coring morphism $\phi:C\rightarrow C'$ between two $R$-corings $(C,\Delta,\epsilon)$ and $(C',\Delta',\epsilon')$ is a coideal.
The only point that I can'...
- 1,601
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Construction of "braided" Hopf algebras
Assume $(H,m,\eta, \Delta, \epsilon, S,r)$ to be a coquasitriangular Hopf-Algebra over $\mathbb C$.
The category $C(H)$ of $H$-comodules is braided monoidal.
Now consider a coaction $\delta: H \...
- 231
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Is the dual of a module naturally a comodule?
This question is basically an extension of the following fact: given a finite dimensional, associative, unital $k$-algebra $A$, then the vector dual $A^*$ is a coassociative, counital coalgebra with ...
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