# Questions tagged [quantum-groups]

In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure.

223 questions
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### What are the differences between submodules and subfactors.

In non-semisimple category, for example the category of representations of a quantum affine algebra $U_q(\hat{g})$, where $g$ is a simple Lie algebra over $\mathbb{C}$. What are the differences ...
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### induction mathematics in bracket of quantum group

By the induction mathematics . How can prove the following [fm,f1m]=0,where f is generators in quantum group and m greter than 3.
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### 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. ...
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### States of a Group Ring

Let $G$ be a finite group and $\mathbb{C}G$ its group ring. Now taking the approach of orangeskid, consider the space $\mathbb{C}G$ as a Hilbert space with orthonormal basis $\delta^g$. $G$ acts on ...
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### What are the applications of quantum shuffle multiplication?

I am writing a research paper on quantum shuffle multiplication, and there is just one piece that I'm missing: I want to give one or several examples of its applications, and so far I have not been ...
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### Relation between integrable representations and highest weight representations.

Let $g$ be a simple Lie algebra and $U_q(g)$ the corresponding quantum group. What are the relation between integrable representations and highest weight representations of $U_q(g)$? Are all highest ...
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### Von Neumann algebraic Quantum Object is direct sum of type I factors

I am looking at the non-standard quantum projective spaces $A:=\mathcal{A}_q(\mathbb{CP}^n(c,d))$ introduced by Dijkhuizen and Noumi. Now I want to show that if I take the von Neumann algebra ...
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### Endomorphism ring of an irreducible comodule

Given a Hopf algebra over $\mathbb{C}$, and a irreducible comodule $V$, I can show that Mor$(V,V) \simeq \mathbb{C}$, where Mor$(V,V)$ is the space of comodule maps from $V$ to $V$. My proof uses that ...