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Results tagged with yang-baxter-equations
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user 45956
In the classical equation, one looks for $R\in\Lambda^2\mathfrak g$ such that $$[R,R]=0,$$ where the bracket is Schouten's bracker in $\Lambda^\bullet\mathfrak g$, the exterior algebra on a Lie algebra $\mathfrak g$. In the quantum one (in its non-parametric form...), one looks for endomorphisms $R:V\otimes V\to V\otimes V$ of tensor squares of vector spaces $V$ such that $$R_{12} \ R_{13} \ R_{23} = R_{23} \ R_{13} \ R_{12},$$
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Accepted
How can I verify that a given solution of the Quantum Yang-Baxter equation is associated to ...
To the best of my knowledge this is a very hard problem and the answer to this question is, unfortunately, open.
A famous example that illustrates this in the context of quantum integrability comes …
- 1,996
2
votes
Accepted
Solution of the Yang-Baxter equation associated to the $U_q[osp(2n+2|2m)^{(2)}]$ Lie superal...
Drinfel'd's quantum double is a construction that produces, given a Hopf algebra, an $R$-matrix that turns it into a quasi-triangular Hopf algebra. You could try working that out to get an $R$-matrix …
- 1,996
3
votes
Weakly involutive $R$-matrices and representations of the symmetric group $S_N$ in restricte...
In the recent physics preprint
Corcoran, De Leeuw and Pozsgay, Integrable models on Rydberg atom chains [arXiv:2405.15848]
the authors study quantum-integrable models related to $R$-matrices with sp …
- 1,996