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Noncommutative analogues of Stein spaces of finite embedding dimension
Cornell University
,
2012.
No. 1204.4936.
In press
We introduce and study holomorphically finitely generated (HFG) Fr\'echet algebras, which are analytic counterparts of affine (i.e., finitely generated) C-algebras. Using a theorem of O. Forster, we prove that the category of commutative HFG algebras is anti-equivalent to the category of Stein spaces of finite embedding dimension. We also show that the class of HFG algebras is stable under some standard constructions. This enables us to give a series of concrete examples of HFG algebras, including Arens-Michael envelopes of affine algebras (such as the algebras of holomorphic functions on the quantum affine space and on the quantum torus), the algebras of holomorphic functions on the free polydisk, on the quantum polydisk, and on the quantum ball. We further concentrate on the algebras of holomorphic functions on the quantum polydisk and on the quantum ball and show that they are isomorphic, in contrast to the classical case. Finally, we interpret our algebras as Fr\'echet algebra deformations of the classical algebras of holomorphic functions on the polydisk and on the ball in C^n.
Pirkovskii A. Y., / Cornell University. Series math "arxiv.org". 2013. No. 1304.1991.
We introduce and study holomorphically finitely generated (HFG) Fr\'echet algebras, which are analytic counterparts of affine (i.e., finitely generated) complex algebras. Using a theorem of O. Forster, we prove that the category of commutative HFG algebras is anti-equivalent to the category of Stein spaces of finite embedding dimension. We also show that the class of ...
Added: May 2, 2013
Pirkovskii A. Y., Journal of Noncommutative Geometry 2015 Vol. 9 No. 1 P. 215-264
We introduce and study holomorphically finitely generated (HFG) Fr\'echet algebras, which are analytic counterparts of affine (i.e., finitely generated) complex algebras. Using a theorem of O. Forster, we prove that the category of commutative HFG algebras is anti-equivalent to the category of Stein spaces of finite embedding dimension. We also show that the class of ...
Added: November 14, 2013
Pirkovskii A. Y., , in : Algebraic Methods in Functional Analysis. The Victor Shulman Anniversary Volume. Operator Theory: Advances and Applications, vol. 233. : Basel : Birkhauser/Springer, 2014. Ch. 10. P. 135-153.
We introduce and study holomorphically finitely generated (HFG) Fr\'echet algebras, which are analytic counterparts of affine (i.e., finitely generated) C-algebras. Using a theorem of O. Forsterфn. We also show that the class of HFG algebras is stable under some standard constructions. This enables us to give a series of concrete examples of HFG algebras, including ...
Added: November 14, 2013
Pirkovskii A. Y., Journal of Noncommutative Geometry 2019 Vol. 13 No. 3 P. 857-886
We introduce and study noncommutative (or "quantized") versions of the algebras of holomorphic functions on the polydisk and on the ball in C^n. Specifically, for each nonzero complex number q we construct Fréchet algebras O_q(D^n) and O_q(B^n) such that for q=1 they are isomorphic to the algebras of holomorphic functions on the open polydisk D^n ...
Added: January 17, 2019
Pirkovskii A. Y., Journal of Physics: Conference Series 2013 Vol. 474 No. 012026 P. 1-14
The classical Poincaré theorem (1907) asserts that the polydisk D^n and the ball B^n in C^n are not biholomorphically equivalent for n ≥ 2. Equivalently, this means that the Fréchet algebras O(D^n) and O(B^n) of holomorphic functions are not topologically isomorphic. Our goal is to prove a noncommutative version of the above result. Given a nonzero complex ...
Added: February 6, 2014
Pirkovskii A. Y., / Cornell University. Series math "arxiv.org". 2015. No. 1508.05768.
We introduce and study noncommutative (or "quantized") versions of the algebras of holomorphic functions on the polydisk and on the ball in C^n. Specifically, for each nonzero complex number q we construct Fréchet algebras O_q(D^n) and O_q(B^n) such that for q=1 they are isomorphic to the algebras of holomorphic functions on the open polydisk D^n ...
Added: August 27, 2015
Pirkovskii A. Y., / Cornell University. Series math "arxiv.org". 2013. No. 1311.0309.
http://arxiv.org/abs/1311.0309 ...
Added: November 14, 2013
Piontkovski D., / Cornell University. Series math "arxiv.org". 2014. No. arXiv:1401.6549.
A noncommutative Grassmanian NGr(m,n) is introduced by Efimov, Luntz, and Orlov in `Deformation theory of objects in homotopy and derived categories III: Abelian categories' as a noncommutative algebra associated to an exceptional collection of n-m+1 coherent sheaves on P^n. It is a graded Calabi--Yau Z-algebra of dimension n-m+1. We show that this algebra is coherent ...
Added: May 13, 2014
Aristov O., A.Yu. Pirkovskii, Journal of Mathematical Analysis and Applications 2020 Vol. 485 No. 2 Article 123817
We characterize open embeddings of Stein spaces and of $C^\infty$-manifolds in terms of certain flatness-type conditions on the respective homomorphisms of function algebras. ...
Added: December 23, 2019
Pirkovskii A. Y., Aristov O., / Cornell University. Series math "arxiv.org". 2019. No. 1908.02117.
We characterize open embeddings of Stein spaces and of $C^\infty$-manifolds in terms of certain flatness-type conditions on the respective homomorphisms of function algebras. ...
Added: August 7, 2019
Sergeev A., Travaux mathematics 2011 Vol. 19 P. 7-26
Строится геометрическое квантование универсального пространства Тейхмюллера. Стандартный метод, используемый для квантования регулярной части пространства Тейхмюллера, не применим ко всему универсальному пространству Тейхмюллера. Для квантования последнего используется подход, основанный на соображениях из квантового анализа Конна ...
Added: February 19, 2013
Pyatov P. N., Journal of Physics A: Mathematical and Theoretical 2016 Vol. 49 No. 41 P. 415202-(25pp)
We develop a construction of the unitary type anti-involution for the quantized differential calculus over GLq (n) in the case ∣q∣ = 1. To this end, we consider a joint associative algebra of quantized functions, differential forms and Lie derivatives over GLq (n)/SLq (n), which is bicovariant with respect to GLq (n)/SLq (n) coactions. We ...
Added: September 30, 2016
Piontkovski D., Journal of Noncommutative Geometry 2016
A noncommutative Grassmanian NGr(m,n) is introduced by Efimov, Luntz, and Orlov in `Deformation theory of objects in homotopy and derived categories III: Abelian categories' as a noncommutative algebra associated to an exceptional collection of n-m+1 coherent sheaves on P^n. It is a graded Calabi--Yau Z-algebra of dimension n-m+1. We show that this algebra is coherent ...
Added: April 14, 2016
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019
Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Amerik E., Verbitsky M., / Cornell University. Series arXiv "math". 2021.
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold ...
Added: April 7, 2022