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arXiv · 2412.04823

Noncommutative complex analytic geometry of a contractive quantum plane

Anar Dosi
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Abstract

In the paper we investigate the Banach space representations of Manin's quantum q-plane for |q| is not 1. The Arens-Michael envelope of the quantum plane is extended up to a Frechet algebra presheaf over its spectrum. The obtained ringed space represents the geometry of the quantum plane as a union of two irreducible components being copies of the complex plane equipped with the q-topology and the disk topology, respectively. It turns out that the Frechet algebra presheaf is commutative modulo its Jacobson radical, which is decomposed into a topological direct sum. The related noncommutative functional calculus problem and the spectral mapping property are solved in terms of the noncommutative Harte spectrum.

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Anar Dosi. 2024-12-06. Noncommutative complex analytic geometry of a contractive quantum plane. https://arxiv.org/abs/2412.04823

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