All Questions
Tagged with hopf-algebras noncommutative-algebra
12
questions
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Finiteness of results in Connes-Kreimer approach
Remark: Although this is technically a physics-related post, the content heavily relies on pure mathematics, so I deemed it more appropriate here.
When reading the papers by Connes and Kreimer (e.g. [...
- 1,713
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56
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Comultiplication on the tensor algebra
Let $k$ be a commutative base ring. We have a category $\operatorname{Mod}_k$ of $k$-modules and a category $\operatorname{grMod}_k$ of $\mathbb{Z}$-graded $k$-modules. Both of these have monoidal ...
- 804
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Left ideals of group algebra $K[\mathbb H]$
I've been studying Hopf-Galois theory, and while writing by myself certain example, I came up with this question:
Let $K$ be a field, and $\mathbb H$ the quaternion group. Is $K[\mathbb H]$ the only ...
- 3,564
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$T(z) e^{-\partial_z} $ for Yangian is a Manin matrix
Let $T(u)$ be the generating matrix of the Yangian $Y(\mathfrak{gl}_n)$ of $\mathfrak{gl}_n$. So we have the identity $[T_{ij}(u),T_{kl}(v)]=\frac{1}{u-v}(T_{kj}(u)T_{il}(v)-T_{kj}(v)T_{il}(u))$.
We ...
- 135
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Hopf "algebroid" structure of a groupoid convolution algebra?
To male thinks simple as possible, lets say we have a discrete group $G.$ Then the then the group algebra $\mathbb{C}[G]$ (of finitely supported complex valued functions on $G$) has a convolution and ...
- 18.4k
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Showing that $U(\mathfrak{sl}_2)$ is a coalgebra
We know that there is a coalgebra structure on $U(\mathfrak{sl}_2)$ as follows for any $z\in \mathfrak{sl}_2$:
$$\Delta(z)=1\otimes z+z\otimes 1, \qquad \epsilon(z)=0.$$
Can someone be so kind to ...
- 570
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Commutativity up to scalar implies commutativity in an algebra
Let $A$ be a (not necessarily commutative) algebra over a field $k$. Suppose that for all $a,b\in A$, we have $kab=kba$, i.e. commutativity up to scalar. Show that then $A$ is commutative.
In the ...
- 1,279
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A certain decomposition of a semisimple Hopf algebra
$\newcommand{\Irr}{\mathrm{Irr}}$
Let $H$ be a finite-dimensional semisimple Hopf algebra over an algebraically closed field $k$, and let $\Irr(H)$ be the set of (choices of representatives of) ...
- 2,075
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Suggestion of research papers
I’m trying to find the research papers related to Hopf algebra over non commutative polynomial rings O( M_n(H))
to get concrete understanding about it. But unfortunately I couldn’t find any ...
- 29
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830
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group-like elements of a Hopf algebra and the group algebra
Suppose we are given a $n$-dimensional Hopf algebra $H$ over field $\mathbb K$. I want to prove that
$H$ contains n distinct group-like elements if and only if there exists a group $G$ such ...
- 1,087
3
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Introductory text on Hopf algebras
Is there an introductory (but as complete as possible) text on Hopf algebras like Abe or Sweedler but working when possible over arbitrary commutative rings instead fields? "Like Abe or Sweedler" ...
- 1,423
5
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545
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An R-matrix in a quasitriangular Hopf algebra
I am new to the theory of Hopf algebra. So I am sorry if the following question has really trivial answer.
Suppose that we have a quasi triangular Hopf algebra with the universal R-matrix $R$. It ...
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