Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with hopf-algebras
Search options not deleted
user 11877
A Hopf algebra is a vector space $H$ over a field $k$ endowed with an associative product $\times:H\otimes_k H\to H$ and a coassociative coproduct $\Delta:H\to H\otimes_k H$ which is a morphism of algebras. Unit $1:k\to H$, counit $\epsilon:H\to k$ and antipode $S:H\to H$ are also required. Such a structure exists on the group algebra $k G$ of a finite group $G$.
9
votes
2
answers
1k
views
Algebra in a category
I am try to understand the concept: an algebra in a category. Let $\mathcal{C}$ be a category and $A$ an object in $\mathcal{C}$. $A$ is an algebra in $\mathcal{C}$ means the multiplication $m: A \oti …
- 6,201
8
votes
1
answer
418
views
Compatibility conditions for Yetter-Drinfeld modules
In the paper, page 28, Definition 4.2.1, the compatibility condition for a Yetter-Drinfeld module over $H$ is
$$
h_{(1)} v_{(-1)} \otimes h_{(2)}.v_{(0)} = (h_{(1)}.v)_{(-1)}h_{(2)} \otimes (h_{(1)}. …
- 6,201
7
votes
1
answer
181
views
How to translate multi-segments to Drinfeld polynomials?
Let $\hat{H}_m=\hat{H}_m(q)$ be the Iwahori-Hecke algebra of $GL_m$, see for example, Section 2. The simple $\hat{H}_m$-modules are parametrized by Zelevinsky's multi-segments, See Section 2.2 of the …
- 6,201
5
votes
1
answer
297
views
Center of quantum affine algebras
Are there some references about the center of quantum affine algebras? I searched on google and only find the paper. In particular, what is the center of $U_q(\widehat{\mathfrak{sl}_2})$. Thank you ve …
- 6,201
4
votes
1
answer
865
views
How to show that the graded dual of the universal enveloping algebra of a free Lie algebra o...
In the article, the universal enveloping algebra of a free Lie algebra on a set X is defined to be the free associative algebra generated by X.
It is said that the graded dual of the universal envel …
- 6,201
4
votes
0
answers
301
views
Does the tensor algebra $T(V)$ of $V$ isomorphic to the symmetric algebra of the free Lie al...
Let $V$ be a finite dimensional vector space. Let $T(V)$ be the tensor algebra over $V$.
Do we have $T(V) \cong S(Lie(V))$ as a graded vector space? Here $S(Lie(V))$ is the symmetric algebra of the …
- 6,201
3
votes
1
answer
123
views
Is $T(V) \rtimes T(V^* \otimes V)$ a bialgebra?
Let $V$ be a vector space and $V^*$ the dual vector space. Let $T(V)$ be the tensor algebra of $V$.
The algebras $T(V)$ and $T(V^* \otimes V)$ are bialgebras. I am trying to find some bialgebra stru …
- 6,201
3
votes
1
answer
242
views
Are there p-adic or finite field analogue of Drinfeld-Jimbo's quantum groups
Drinfeld-Jimbo's quantum groups are associated algebras over the field of complex numbers. Are there some references about the analogue of Drinfeld-Jimbo's quantum groups over a p-adic field or a fini …
- 6,201
3
votes
1
answer
682
views
Deformation of a Hopf algebra
A deformation of a Hopf algebra is defined as follows.
On page 171 of the book a guide to quantum groups, Remark 2, it is said that Any deformation of a Hopf algebra $A$ as a bialgebra is automatica …
- 6,201
3
votes
2
answers
243
views
How to show that Yetter-Drinfeld condition is equialent to $\Psi$ is a braiding
Let $H$ be a Hopf algebra and $V$ a right $H$-module and right $H$-comodule. The module $V$ is a Yetter-Drinfeld module over $H$ if and only if
\begin{align}
( v \triangleleft h_{(2)} )_{(0)} \otimes …
- 6,201
2
votes
0
answers
310
views
Module algebras and comodule algebras
Let $H$ be a Hopf algebra and $A$ an algebra. Let $H^*$ be the dual Hopf algebra of $H$. Then by Proposition 1.6.11 in the book Foundations of Quantum Group Theory by Shahn Majid, $A$ is a right $H$-c …
- 6,201
2
votes
1
answer
179
views
Is the cross product $A \rtimes H$ a bialgebra?
Let $H$ be a bialgebra and $A$ a $H$-module algebra. The cross product $A \rtimes H$ is defined as follows. As a vector space $A \rtimes H = A \otimes H$. The multiplication on $A \rtimes H$ is define …
- 6,201
2
votes
1
answer
93
views
Are braided commutators primitive elements of a braided Hopf algebra?
Let $H$ be a braided Hopf algebra. The multiplication on $H \otimes H$ is defined by $(a \otimes b)(c \otimes d) = a \Psi(b \otimes c) d$, $a,b,c,d \in H$.
Let $H = T(V)$. There is a algebra map $\D …
- 6,201
1
vote
How to translate multi-segments to Drinfeld polynomials?
This is described in equation (5.2) in the paper which follows from the paper: Quantum affine algebras and affine Hecke algebras.
- 6,201
1
vote
0
answers
127
views
References of an operator $T: V \otimes V \to V \otimes V$
Let $V$ be a vector space with a basis $v_1, \ldots, v_n$ and let $X_{ij} = v_i \otimes v_j$. Then $X_{ij}, i,j=1,\ldots, n$, is a basis of $V \otimes V$. Let $T: V \otimes V \to V \otimes V$ be the l …
- 6,201