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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.04823 |
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| _version_ | 1866910729937879040 |
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| author | Dosi, Anar |
| author_facet | Dosi, Anar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04823 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noncommutative complex analytic geometry of a contractive quantum plane Dosi, Anar Functional Analysis Operator Algebras 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. |
| title | Noncommutative complex analytic geometry of a contractive quantum plane |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2412.04823 |