Holomorphic Structures on the Quantum Projective Line
By Masoud Khalkhali, Giovanni Landi, W. D. Suijlekom. 2009
71 citations recorded by the source corpus.
We show that much of the structure of the 2-sphere as a complex curve survives the q-deformation and has natural generalizations to the quantum 2-sphere—which, with additional structures, we identify with the quantum projective line. Notably among these is the identification of a quantum homogeneous coordinate ring with the coordinate ring of the quantum plane. In parallel with the fact that positive Hochschild cocycles on the algebra of smooth functions on a compact oriented 2-dimensional manifold encode the information for complex structures on the surface, we formulate a notion of twisted positivity for twisted Hochschild and cyclic cocycles and exhibit an explicit twisted positive Hochschild cocycle for the complex structure on the sphere.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/836b01e082ba10ed46003add032c59c2e963d42f
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Noncommutative K\"ahler Structures on Quantum Homogeneous Spaces (2011, methodology): “ calculus, which is uniquely characterised by a simple set of natural axioms [13, 14]. These calculi have already served as the motivating examples for the theory of noncommutative complex structures [1, 17, 31]. Metric phenomena have appeared a number of times in the literature on the noncommutativ”