Questions tagged [r-matrix]
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Question regarding orthogonality of a map
I am reading the materials discussed in lecture $5$ from the lecture notes on quantum groups about Belavin-Drinfeld classification theorem written by Pavel Etingof and Oliver Schiffmann.
In the first ...
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R-matrices and symmetric fusion categories
Given a $\mathbb{C}$-linear braided fusion category $\mathcal{C}$ containing a fusion rule of the form e.g.
\begin{equation}X\otimes Y\cong A\oplus B \oplus C\end{equation}
(where $A,B, C, X$ and $Y$ ...
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Classification of quasitriangular Hopf algebras
The classification of hopf algebras is a big and open problem, containing various subproblems (such as: the classification of groups, of Lie algebras, the study of special classes such as (co)...
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Yang-Baxter equation for the asymmetric simple exclusion process (ASEP)
On page 14 of Craig Tracy's slides on ASEP, it states that the $n$-particle boundary condition can be reduced to the 2-particle boundary condition due to the fact that the $S$-matrix satisfies the ...
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R-matrices, crystal bases, and the limit as q -> 1
I am seeking references for precise statements and rigorous proofs of some facts about the actions of quantum root vectors and $R$-matrices on crystal bases for finite-dimensional representations of ...
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Is there a good reference for how ribbon structures change when one switches coproducts?
I'm just going assume readers are familiar with the notions of R-matrix and ribbon categories.
Given a quasi-triangular Hopf algebra $A$ with $R$-matrix $R$, one can construct the co-opposite Hopf ...
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What structure on a monoidal category would make its 2-category of module categories monoidal and braided?
So, many of us know the answer to "what kind of structure on an algebra would make its category of representations braided monoidal": your algebra should be a quasi-triangular Hopf algebra (maybe if ...
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What's the right object to categorify a braided tensor category?
The yoga of categorification has gained a lot of popularity in recent years, and some techniques for it have made a lot of progress. It's well-understood that, for example, a ring is probably ...
- 43.2k
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Are supervector spaces the representations of a Hopf algebra?
Supervector spaces look a lot like the category of representations of $\mathbb{Z}/2\mathbb{Z}$ - the even part corresponds to the copies of the trivial representation and the odd part corresponds to ...
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An inner product that makes the R-matrix unitary
So, if you talk to the right people, they will tell you that the braiding of the category of representations of a quantum group are not unitary and that one can fix this by taking a different commutor ...
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How does one think about the "off-diagonal" part of the $R$-matrix?
The universal $R$-matrix of a quantized universal enveloping algebra is typically written as the product of two terms, one only involving elements of the Cartan, and one only involving elements of the ...
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