All Questions
Tagged with hopf-algebras mp.mathematical-physics
8 questions
3
votes
0
answers
65
views
A combinatorial Dyson-Schwinger equation, tree diagrams, and compositional inversion of a Laurent series
In "Tree hook length formulae, Feynman rules and B-series", Bradley Jones and Karen Yeats state on pg. 9:
Combinatorial Dyson-Schwinger equations are functional equations with solutions in
$...
- 10.5k
5
votes
1
answer
80
views
Weakly involutive $R$-matrices and representations of the symmetric group $S_N$ in restricted subspaces of $V^{\otimes N}$
An $R$-matrix is a matrix $R\in\operatorname{End}(V\otimes V)$ (where $V$ is a finite dimensional vector space) that solves the Yang–Baxter equation
$$R_{12}R_{23}R_{12}=R_{23}R_{12}R_{23},$$
where ...
- 727
8
votes
1
answer
311
views
How does the Tannaka duality work for weak Hopf algebras and fusion categories?
I'm a physicist and not yet an expert in fusion category. I've heard that it's possible to reconstruct a weak Hopf algebra from its category of representations, and would like to know how this works ...
- 727
5
votes
1
answer
575
views
Is there another quantum deformation of sl(2)?
By looking at defining relations of standard deformation of $\mathfrak{sl}_2$, which are:
$$
[E,F] = \frac{q^{H}-q^{-H}}{q-q^{-1}}, \quad [H,E] = 2E, \quad \text{ and } \quad [H,F] = -2F,
$$
some ...
- 53
17
votes
4
answers
1k
views
Braided Hopf algebras and Quantum Field Theories
It is well-known, that there are a lot of applications of classical Hopf algebras in QFT, e.g. Connes-Kreimer renormalization, Birkhoff decomposition, Zimmermann formula, properties of Rota-Baxter ...
- 797
6
votes
1
answer
308
views
Compact Quantum Groups and FRT-Algebras
As is well known, every compact quantum group in the sense of Woronowicz has a dense Hopf $*$-sub-algebra. For the case of $q-SU(n)$ (among others) this Hopf $*$-sub-algebra is an FRT-algebra, which ...
- 159
13
votes
2
answers
1k
views
Hopf Algebra for a physicist
Hello,
for my bachelor's thesis I need to understand the Hopf Algebra of Feynman Diagrams. As I have only litte knowledge in Algebra by now I wanted to ask where I could start and what preknowledge I ...
- 133
19
votes
1
answer
2k
views
Connes-Kreimer Hopf algebra and cosmic Galois group
Hi,
I'm interested in the relation between the two following constructions motivated by renormalization:
Connes-Kreimer gives an interpretation of the renormalization procedure in the framework of ...
- 8,524