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Results tagged with quantum-groups
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user 13215
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.
55
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Accepted
What is quantum algebra?
Quantum algebra is an umbrella term used to describe a number of different mathematical ideas, all of which are linked back to the original realisation that in quantum physics, one finds noncommutativ …
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17
votes
3
answers
1k
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Isomorphisms of quantum planes
Let $k$ be a field and $q\in k^{*}$. The quantum plane $k_{q}[x,y]$ is the algebra $k\langle x,y\rangle/\langle xy=qyx \rangle$ (i.e. the quotient of the free non-commutative $k$-algebra on two varia …
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9
votes
Accepted
Computing in quantum groups
There is the package QuaGroup by de Graaf for both GAP and Magma: see QuaGroup. I've used it in both systems and found it to be extremely helpful. Since there's a GAP package, you also have the opti …
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7
votes
quantum groups... not via presentations
Some possible partial answers might be:
one could follow Lusztig and do away with the Lie algebra completely, just starting from a root datum. Then do some geometry...
Majid's reinterpretation of L …
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6
votes
Understanding definition of quantization of a Poisson-Hopf algebra
You didn't give the definition of $A_h$ but if you look there, you should see that elements of it are formal power series in the parameter $h$ with coefficients from $A$. Then "mod $h$" means "take t …
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4
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Why are quantum groups so called?
For quantum matrices and related objects specifically, I heartily recommend the opening chapters of "Lectures on Algebraic Quantum Groups" by Brown and Goodearl. I hesitate to write any more details, …
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