Noncommutative Complex Structures on Quantum Homogeneous Spaces
Quantum Algebra
2015-11-06 v9 Algebraic Geometry
Abstract
A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully flat quantum homogeneous spaces. A number of basic results are established, producing a simple set of necessary and sufficient conditions for noncommutative complex structures to exist. Throughout, the family of quantum projective spaces, endowed with the Heckenberger--Kolb calculus, is taken as the motivating set of examples.
Cite
@article{arxiv.1108.2374,
title = {Noncommutative Complex Structures on Quantum Homogeneous Spaces},
author = {Réamonn Ó Buachalla},
journal= {arXiv preprint arXiv:1108.2374},
year = {2015}
}
Comments
Final version. In Press