Семинары: A. A. Dosi, Noncommutative complex analytic geometry of a contractive quantum plane

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Семинар «Алгебры в анализе» 26 апреля 2024 г. 18:00, г. Москва, доклад состоится на платформе Zoom, ссылка предоставляется по запросу

Noncommutative complex analytic geometry of a contractive quantum plane А. А. Доси
https://youtu.be/Ma-3A85-7-g Аннотация: In the present talk we discuss the Banach space representations of Manin's quantum $q$-plane for $\|q\|\ne 1$. The Arens-Michael envelope of the quantum plane is extended up to a Fréchet 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 Fréchet 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. Язык доклада: английский