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Quantum Complex Structures

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Quantum Riemannian Geometry

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 355))

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Abstract

This chapter formulates noncommutative complex structures along the lines of classical complex manifold theory including a bigrading of the exterior algebra to give a double complex. We then study holomorphic modules and implications for cohomology theories. Examples include the noncommutative torus and the q-sphere.

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Authors and Affiliations

  1. Department of Mathematics, Swansea University, Swansea, UK

    Edwin J. Beggs

  2. School of Mathematical Sciences, Queen Mary University of London, London, UK

    Shahn Majid

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Beggs, E.J., Majid, S. (2020). Quantum Complex Structures. In: Quantum Riemannian Geometry. Grundlehren der mathematischen Wissenschaften, vol 355. Springer, Cham. https://doi.org/10.1007/978-3-030-30294-8_7

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