# Questions tagged [hopf-algebra]

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### Are there concrete examples of, and ways to visualise, quantum groups?

I'm trying to get my head around quantum groups, and the basic ideas that (a) they're actually algebras, and (b) they have ''deformed'' relations such as $$ab=ba\rightarrow ab=qba$$ are all fine and ...
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### Hopfion with only in-plane vortex rather than skyrmion along the torus?

A simple torus-like hopfion with hopf charge $Q_H=1$ will typically exhibit a skyrmion at each slice cutting the toroidal circle. What if the skyrmion is replaced by an in-plane 2D vortex, i.e., we ...
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### Hopf algebras vs Fusion categories for topological order

Disclaimer: Before I begin with the question I want to warn that some people would argue that it is a math question and not a physics question. However, it finds it origins in the study of topological ...
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### When do the solutions of combinatorial Dyson-Schwinger equations generate a Hopf subalgebra?

Say I have a set of combinatorial Dyson-Schwinger equations of the form \begin{align} X_1 &= \mathbb{1} + \alpha B_+^a (f_1(X_1,...X_N)) \\ & ... \tag{1} \\ X_N &= \mathbb{1} + \alpha ...
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### External structure in BPHZ/Hopf algebraic renormalization of QED

I'm currently trying to understand and reproduce the Hopf-algebraic renormalization of QED presented by Walter D. Van Suijlekom. I don't understand why he chooses these external structures in (2), (7),...
• 33
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### Hopf Algebras in Quantum Groups

In the theory of quantum groups Hopf algebras arise via the Fourier transform: A third point of view is that Hopf algebras are the next simplest category after Abelian groups admitting Fourier ...
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### Boson calculus and Maximum Weight State

I'm just going over a few past exams for tomorrow, and I've come across a question that I'm having quite a bit of difficulty with. Let $\left|0\right\rangle$ denote the Fock vacuum state so that \$...
• 205
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### What are the uses of Hopf algebras in physics?

Hopf algebra is nice object full of structure (a bialgebra with an antipode). To get some idea what it looks like, group itself is a Hopf algebra, considered over a field with one element ;) usual ...
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