All Questions
Tagged with qa.quantum-algebra noncommutative-geometry
8 questions
4
votes
0
answers
338
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Quantization of $S^2$ as $C^*$-algebra?
The general context for the question - is belief that quantization of compact symplectic manifolds can be endowed with the structure of $C^*$-algebra (see MO230695).
The particular question is about ...
- 24.9k
38
votes
6
answers
4k
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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
13
votes
6
answers
2k
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Hopf algebras arising as Group Algebras
Every commutative $C^*$-algebra is isomorphic to the set of continuous functions, that vanish at infinity, of a locally compact Hausdorff space. Every commutative finite dimensional Hopf algebra is ...
- 1,462
9
votes
4
answers
1k
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Kontsevich, and Geometric, Quantization and the Podles sphere
There exist a large family of noncommutative spaces that arise from the quantum matrices. These algebraic objects $q$-deform the coordinate rings of certain varieties. For example, take quantum $SU(2)$...
- 1,462
9
votes
0
answers
268
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Existence/characterization/properties of $C^*$-algebras which "are" quantization of compact symplectic manifolds?
Understanding of "quantization" achieved much progress recent years, especially after Kontsevich breakthrough on deformation quantization, where he proved one-to-one correspondence between Poisson ...
- 24.9k
5
votes
1
answer
2k
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Homotopic morphisms between curved A-infinity algebras
I know how to think about (curved) $A_\infty$-algebras 'geometrically', i.e. via formal non-commutative geometry in the sense of Kontsevich etc. I also know how to think about $A_\infty$-morphisms in ...
- 460
4
votes
1
answer
275
views
What are the norms of the generators of the standard Podleś sphere?
Fix a real number $0<q<1$. We consider the standard Podles sphere $A_q$ as the universal unit $C^*$-algebra generated by $a$ and $b$ with relations
\begin{equation*}
\begin{split}
&a=a^*,~ ...
- 9,019
0
votes
1
answer
144
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Is a NC sphere a (one point) compactification of a NC plane?
Inspired by this question About noncommutative sphere and inspired by the fact that the classical sphere is the one point compactificatiin of $\mathbb{R}^2$ we ask the question below:
Is the non ...
- 356