# Tagged Questions

For questions about Hopf algebras and related concepts, such as quantum groups.

44 views

### Why not use the Cartesian product for the monoidal category of modules? Why use the tensor product?

At least for vector spaces, the Cartesian product is a direct sum (categorical product and coproduct) operation. Looking at the definition of monoidal category on Wikipedia, the Cartesian product/...
28 views

### Hopf gradings on complex commutative group rings

Let $G$ be a finite abelian group. The complex group ring $\mathbb{C}G$ admits a structure of Hopf algebra when the multiplication is the usual multiplication in a group ring and the co-multiplication ...
45 views

### Inverse limit of Hopfalgebras

My Question relates to Corollary 2.7 of http://www.jmilne.org/math/xnotes/tc.pdf So Let $k$ be a field and $\mathbb{G}_i$ be an projective system of affine $k$-groupschemes. I want to know if the ...
30 views

### Is the tensor product of two Yetter-Drinfeld modules a Yetter-Drinfeld module?

Let $U,V$ be two Yetter-Drinfeld modules over a bialgebra $H$. Is $U \otimes V$ a Yetter-Drinfeld modules over $H$? Thank you very much.
20 views

### When $H$ is a Yetter-Drinfeld module over itself? [closed]

Let $H$ be a bialgebra. When $H$ is a Yetter-Drinfeld module over itself? Thank you very much.
20 views

### How to show that Yetter-Drinfeld condition is equivalent to the condition of $H$-action commutes with braiding?

Let $H$ be a bialgebra and ${}_H^H YD$ the category of Yetter-Drinfeld modules over $H$. It is said that Yetter-Drinfeld condition is equivalent to the condition of $H$-action commutes with braiding. ...
12 views

### Easy References for understanding Grossmann and Larson rooted trees?

I am an undergraduate student doing a project on rooted trees. I was wondering if anyone would know any easy to understand references that explains Grossman and Larson's Hopf Algebra on rooted trees? ...
48 views

69 views

51 views

48 views

### What natural monoidal structure and braiding exists on the category of modules of the convolution algebra of an action groupoid?

Let $S$ be a set with an action $\triangleright$ of a finite group $G$. The action groupoid $S // G$ has as objects the set $S$, and the morphisms from $s_1$ to $s_2$ are just the $g \in G$ that ...
27 views

### Homomorphisms of quantum spaces

Suppose we have a look at the Hopf $*$-algebra $U_q(sl(2))$ and the Hopf $*$-algebra $A_q(\widetilde{S}^3)$ introduced in the paper: http://arxiv.org/pdf/q-alg/9605017v1.pdf. I want to find a relation ...
42 views

### If $N$ is a subcomodule of $M$, then the H-submodule generated by $N$ is a H-Hopf-module of $M$.

Let $H$ be a Hopf algebra with $S$ its antipode and let $M$ be a right $H$-Hopf-module. We will write $\rhd$ the action of the left $H^*$-module on $M$ induced by the structure of right $H$-module, ...
18 views

### Analog of Hopf algebra structure for field of fractions

Let $G$ be a linear algebraic group. Then there is an additional structure on $k[G]$ called structure of Hopf algebra. Question: Is there an extra structure on field of fractions $k(G)$?
We know that representations of a lie algebra $\mathfrak{g}$ can be studied by looking at the representations of the associative algebra $\mathcal{U}(\mathfrak{g})$, the universal enveloping algebra. ...