All Questions
Tagged with yang-baxter-equations hopf-algebras
3 questions
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
1
vote
0
answers
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Problem in understanding Theorem $6.2.9$ from Chari and Pressley
The theorem I am referring to here says that if we start with a Lie bialgebra $\mathfrak g$ determined by some skew-symmetric element $r \in \mathfrak g \otimes \mathfrak g$ satisfying classical Yang-...
- 199
6
votes
2
answers
320
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Involutive solutions to the Yang-Baxter equation (and triangular Hopf algebras)
I'm interested in solutions to the Yang-Baxter equation
$$R_{12}R_{23}R_{12}=R_{23}R_{12}R_{23},$$
that are involutive $R^2_{12}=1$. Or put it another way, I'm interested in representations of the ...
- 727