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Results tagged with qa.quantum-algebra
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user 3696
Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
6
votes
Accepted
Kontsevich, and Geometric, Quantization and the Podles sphere
As far as I understand, the flag manifolds with Kahler structures mentioned in the question are simply coadjoint orbits of compact Lie groups with the Kirillov-Kostant-Souriau bracket, so their quanti …
- 3,929
22
votes
What does "quantization is not a functor" really mean?
This is meant to explain a bit more some of the things that were already mentioned before.
Quantization of Lie bialgebras is indeed a functor, as was shown in my work with Kazhdan. However, the Kons …
- 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
5
votes
What is an algebraic group over a noncommutative ring?
I'd like to add that there is an interesting paper arXiv:math/0701399
that discusses Lie algebras and groups over noncommutative rings.
- 3,929
12
votes
Can the Quantum Torus be realized as a Hall Algebra?
As far as I understand, the Hall algebra of a category (say, with finite length of objects) is graded by the Grothendieck monoid of this category, spanned by simple objects over $\Bbb Z_+$, and it mus …
- 3,929
7
votes
Accepted
Comparing two similar procedures for quantizing a Casimir Lie algebra
The second construction (Lie bialgebra quantization) in fact also uses a Drinfeld associator. The braided tensor categories obtained in these two ways are equivalent, since the quasitriangular QUE alg …
- 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