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Results tagged with qa.quantum-algebra
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user 750
Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
38
votes
6
answers
4k
views
Why Drinfel'd-Jimbo-type quantum groups?
Hopf algebras are pretty easy to motivate, as a not-necessarily-commutative generalization of the ring of functions on an algebraic group (and there are many other ways in which they come up). I like …
- 13k
12
votes
1
answer
2k
views
Can the Quantum Torus be realized as a Hall Algebra?
Background
The Quantum Torus
Let $q$ be an arbitrary complex number, and define (the algebra of) the quantum torus to be
$$T_q:=\mathbb{C}\langle x^{\pm 1},y^{\pm 1}\rangle/xy-qyx$$
For $q=1$, this is …
- 13k
6
votes
Why Drinfel'd-Jimbo-type quantum groups?
So, here's some of my own investigation into this. Define the n-th partial flag variety $Fl_n(\mathbb{C}^m)$ to be the set of all n-step partial flags
$$F_0 \subseteq F_1 \subseteq ... \subseteq F_n …
- 13k