All Questions
Tagged with hopf-algebras reference-request
23
questions
2
votes
1
answer
115
views
What is the dual Hopf algebra of T(V)?
I am reading "Geometric versus Non-Geometric Rough Paths" by Martin Hairer and David Kelly. I don't know much about Hopf algebras but $T(V)$ is the one example I'm comfortable with so far ...
- 1,344
1
vote
0
answers
55
views
Is Spec $\mathbb{C}[-] $ exact?
I am struggling to find a reference to understand the following fact.
Let $0 \to A \to B \to C \to 0$ be a short exact sequence of abelian groups.
I first apply the functor $\mathbb{C}[-]$ taking ...
2
votes
1
answer
128
views
Is the kernel of an action of a Hopf algebra on an algebra a biideal?
S.Dascalescu, C.Nastasescu and S.Raianu define the action of a Hopf algebra $H$ on an (associative) algebra $A$ as a map $H\times A\owns (h,a)\mapsto h\cdot a\in A$ which
is an action of $H$ on $A$ ...
- 2,463
2
votes
0
answers
188
views
Two finite groups are isomorphic if and only if their group algebras are isomorphic as Hopf algebras
Is there a good textbook reference for the proof of:
Two finite groups $G$ and $H$ are isomorphic as groups if and only if their group algebras over the same field $K$ are isomorphic as Hopf ...
- 540
3
votes
0
answers
150
views
Tensor product of bialgebras in a braided monoidal category
Let $(\mathcal{C},\otimes,\mathbb{I},\alpha,\lambda,\rho,c)$ be a braided monoidal category. By this I mean a (not necessarily strict) monoidal category $(\mathcal{C},\otimes,\mathbb{I},\alpha,\lambda,...
- 2,872
1
vote
1
answer
115
views
Is the Drinfeld center of an abelian monoidal category still abelian?
I am interested in knowing if the category $^H_H\mathcal{YD}$ of left-left Yetter-Drinfeld modules over an infinite dimensional Hopf algebra $H$ is an abelian category or not.
The answer is ...
- 2,872
2
votes
0
answers
42
views
Reference Request: Proof of $\mathrm{H}(\mathrm{Prim}\,\mathcal{H}) \cong \mathrm{Prim}\,\mathrm{H}(\mathcal{H})$ for cocommutative dg-Hopf algebras
In Loday’s book Cyclic Homology the following theorem appears:
A.9 Theorem.
On a cocommutative differential graded Hopf algebra $\mathcal{H}$ over a characteristic zero field $k$ the homology and ...
- 16.6k
4
votes
2
answers
228
views
Reference Request: Differential Graded Hopf Algebras
To prepare an upcoming seminar talk I’m trying to find introductory texts on differential graded Hopf algebras (over a field $k$).
My knowledge of Hopf algebras encompasses roughly the first 5 ...
- 16.6k
4
votes
0
answers
140
views
Lie algebra of a compact Lie group
Let $\mathcal{G}$ be a compact (real) Lie group. We know that the Lie algebra $\mathfrak{g}$ of $\mathcal{G}$ is, by definition, the space of all left-invariant (smooth) vector fields over $\mathcal{G}...
- 2,872
8
votes
1
answer
1k
views
Convolution in Hopf algebras
For each Hopf algebra $H$ its space ${\mathcal L}(H)$ of operators $A:H\to H$ is usually endowed with the operation of convolution by the identity
$$
A*B = \mu \circ (A\otimes B)\circ \varDelta
$$
...
- 2,463
2
votes
1
answer
438
views
Book recommendation for Hopf algebras [duplicate]
My motivation for studying Hopf algebras is twofold:
I'm interested in representation theory and the algebraic structure of group rings.
I will also take a course on algebraic groups soon and I ...
- 21.8k
3
votes
0
answers
56
views
Uniqueness of quantizations
When studying quantum groups, in particular quantized universal enveloping algebras, people will tell you that such a quantization is in some sense unique. More specifically, you might hear that a ...
- 12.6k
2
votes
2
answers
98
views
References on $\text{Rep}(H)$ is a braided tensor category
There is the statement:
Let $H$ be a Hopf algebra, then $\text{Rep}(H)$ is a braided tensor category.
Does anybody know some references on this? Is it covered in Kassel's 'Quantum Groups'?
user497572
18
votes
1
answer
3k
views
Good Introduction to Hopf Algebras with Examples
I want to learn more about hopf algebras but I am having trouble finding a down to earth introduction to the subject with lots of motivation and examples. My algebra knowledge ranges from Dummit and ...
- 3,253
6
votes
1
answer
276
views
Two Hopf algebras associated to a linear algebraic group
Let $G$ be a linear algebraic group over a field $k$, then there are two different Hopf algebras associated to $G$. First is just coordinate ring $k[G]$of $G$. This is a commutative Hopf algebra. But ...
- 6,407