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Usual torus vs. Non-commutative torus aka quantum torus.
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Classroom Contents
An Introductory Mini Course into Quantum Toric Geometry Lecture I - Day 1
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- 1 Intro
- 2 Recall the basic structure of a (compact) toric variety (over C)
- 3 In general...
- 4 What are non-commutative spaces? (Gelfand duality)
- 5 Usual torus vs. Non-commutative torus aka quantum torus.
- 6 Constructing the Kronecker foliation.
- 7 Exercise.
- 8 We need Groupoids, objects that generalize groups actions (groups).
- 9 Associativity...
- 10 Internal facts... (Logic).
- 11 Natural transformations.
- 12 Group Actions produce Groupoids
- 13 Lie Groupoids
- 14 Étale Groupoids.
- 15 Morita equivalence.
- 16 Stacks associated to foliations.
- 17 Morita equivalence of algebras.
