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Complex geometry of quantum cones / Tomasz Brzezinski

Fortschritte der Physik, Volume: 62, Issue: 9-10, Pages: 875 - 880

Swansea University Author: Tomasz, Brzezinski

DOI (Published version): 10.1002/prop.201400051

Abstract

The algebras obtained as fixed points of the action of the cyclic group ZN on the coordinate algebra of the quantum disc are studied. These can be understood as coordinate algebras of quantum or non-commutative cones. The following observations are made. First, contrary to the classical situation, t...

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Published in: Fortschritte der Physik
Published: 2014
Online Access: http://arxiv.org/abs/1406.2517
URI: https://cronfa.swan.ac.uk/Record/cronfa20516
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Abstract: The algebras obtained as fixed points of the action of the cyclic group ZN on the coordinate algebra of the quantum disc are studied. These can be understood as coordinate algebras of quantum or non-commutative cones. The following observations are made. First, contrary to the classical situation, the actions of ZN are free and the resulting algebras are homologically smooth. Second, the quantum cone algebras admit differential calculi that have all the characteristics of calculi on smooth complex curves. Third, the corresponding volume forms are exact, indicating that the constructed algebras describe manifolds with boundaries.
College: College of Science
Issue: 9-10
Start Page: 875
End Page: 880