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Results tagged with quantum-groups
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user 3696
Questions about algebraic structures known as quantum groups, and their categories of representations. Quasitriangular Hopf algebras and their Drinfel'd twists, triangular Hopf algebras, $C^\star$ quantum groups, h-adic quantum groups, various semisimplified categories at roots of unity which are called "quantum groups", bicrossproduct quantum groups, and quantum groups coming from braided tensor categories.
17
votes
Accepted
What is the relation between quantum symmetry and quantum groups?
Yes, quantum groups naturally arise in many physics problems. E.g. solutions of the quantum Yang-Baxter equation appear as scattering matrices of integrable 2-dimensional quantum field theories (see " …
- 3,929
14
votes
Accepted
Calculating 6j-symbols (aka Racah-Wigner coefficients) for quantum groups
We can also use partitions ($k$) (symmetric powers) instead of ($1^k$) on one or two of the edges. This still gives just scalars, but includes the full story for sl(2).
This problem seems to be equi …
- 3,929
6
votes
Solutions of the Quantum Yang-Baxter Equation
Maybe I should point out the paper by Hietarinta "Solving the two-dimensional constant quantum Yang--Baxter equation", which can be found on the web. There, he completely classifies constant solutions …
- 3,929
6
votes
Are there interesting monoidal structures on representations of quantum affine algebras?
The poles of the R-matrices for quantum affine algebras are the price to pay for the abovementioned simplification - the braiding becomes symmetric under q-deformation.
If there were no poles, the ca …
- 3,929