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## Pontryagin duality and topological algebras, in: “Topological Algebras, their Applications and Related Topics"

Vol. 67.
IMPAN, 2005.

191574970

Academic editor: K. Jarosz, A. Soltysiak

Under the general editorship: K. Jarosz, A. Soltysiak

Akbarov S. S., De Gruyter, 2022

The term "stereotype space" was introduced in 1995 and is used for a category of locally convex spaces with surprisingly elegant properties. Its study gives an unexpected point of view on functional analysis that brings this field closer to other main branches of mathematics, namely, to algebra and geometry.
This volume contains:
the foundations of the theory ...

Added: June 1, 2022

191574970, Mathematical notes 1999 Vol. 66 No. 6 P. 941-944

Added: September 23, 2016

191574970, Functional Analysis and Its Applications 1999 Vol. 33 No. 2 P. 68-73

Added: September 23, 2016

191574970, Journal of Mathematical Sciences 2003 Vol. 113 No. 2 P. 179-349

Added: September 23, 2016

191574970, Mathematical notes 2013 Vol. 94 No. 5 P. 814-815

Added: September 23, 2016

Свойство стереотипной аппроксимации для алгебр C(M) непрерывных функций на метрических пространствах

Akbarov S. S., Математические заметки 2020 Т. 108 № 3 С. 452-456

We prove that the space C(M) of continuous functions on an arbitrary complete (not necessarily locally compact) metric space M has the stereotype approximation property. ...

Added: October 25, 2020

Akbarov S. S., Итоги науки и техники. Современная математика и ее приложения. Тематические обзоры 2017 Т. 129 С. 3-133

Since the first optical instruments have been invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way of formalizing this idea in mathematics is the construction that assigns to an arbitrary object A in a category K its envelope Env^Ω_ Φ A in a given class Ω ...

Added: October 21, 2018

Akbarov S. S., Итоги науки и техники. Современная математика и ее приложения. Тематические обзоры 2017 Т. 130 С. 3-112

Since the first optical instruments have been invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way of formalizing this idea in mathematics is the construction that assigns to an arbitrary object A in a category K its envelope Env^Ω_ Φ A in a given class Ω ...

Added: October 21, 2018

191574970, Dissertationes Mathematicae 2016 Vol. 513 P. 1-188

An envelope in a category is a construction that generalizes the operations of “exterior completion”, like completion of a locally convex space, or the Stone–Čech compactification of a topological space, or the universal enveloping algebra of a Lie algebra. Dually, a refinement generalizes the operations of “interior enrichment”, like bornologification (or saturation) of a locally ...

Added: September 23, 2016

191574970, Nova Science Publishers, 2000

Added: September 23, 2016

Бунина Е. И., Trushin D., Tsvetkov M. V., Journal of Mathematical Sciences 2015 Vol. 206 No. 6 P. 629-633

In this paper, we construct noncommutative algebras over a square-closed field such that the unitary linear groups over these algebras decompose to nontrivial free products. In particular, we give an example in which the elementary unitary subgroup belongs to one of these factors. ...

Added: February 20, 2018

191574970, Mathematical notes 2015 Vol. 97 No. 3 P. 489-492

A smooth envelope of a topological algebra is introduced, and the following result is announced: the smooth envelope of a given subalgebra A in C∞(M) coincides with C∞(M) if and only if A has the same tangent bundle as M. ...

Added: September 23, 2016

191574970, Izvestiya. Mathematics 2000 Vol. 64 No. 4 P. 3-46

We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis. ...

Added: September 23, 2016

191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90

It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...

Added: September 23, 2016

191574970, Functional Analysis and Its Applications 2000 Vol. 34 No. 1 P. 60-63

Added: September 23, 2016

Zinova P., Функциональный анализ и его приложения 2020 Т. 54 № 3 С. 73-93

A weight system is a function on chord diagrams that satisfies the so-called four-term
relations. Vassiliev’s theory of finite-order knot invariants describes these invariants in terms of
weight systems. In particular, there is a weight system corresponding to the colored Jones polynomial.
This weight system can be easily defined in terms of the Lie algebra sl2, but this ...

Added: December 10, 2020

Akbarov S. S., Journal of Mathematical Sciences 2017 Vol. 227 No. 6 P. 669-789

Since the first optical instruments have been invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way of formalizing this idea in mathematics is the construction that assigns to an arbitrary object A in a category K its envelope Env^Ω_ Φ A in a given class Ω ...

Added: October 21, 2018

S. S. Akbarov, Journal of Algebra and its Applications 2020 Vol. 19 No. 6 P. 1-28

We prove several properties of kernels and cokernels in the category of augmented involutive
stereotype algebras: 1) this category has kernels and cokernels, 2) the cokernel is preserved under the
passage to the group stereotype algebras, and 3) the notion of cokernel allows to prove that the continuous
envelope Env C*(Z · K) of the group algebra of ...

Added: June 8, 2019

Akbarov S. S., Journal of Operator Theory 2022 Vol. 88 No. 1 P. 3-36

In 2013, Yu.N. Kuznetsova constructed a duality theory for Moore groups, based on the idea of a continuous envelope of topological algebra and having the advantage over the existing theories that its enveloping category consists of Hopf algebras in the classical sense. Unfortunately, her work contains several errors, due to which her theory can be considered proved only for ...

Added: August 10, 2022

Pirkovskii A. Y., / Cornell University. Series math "arxiv.org". 2011. No. 1101.0166.

Given a Hopf algebra H and an H-module algebra A, we explicitly describe the Arens-Michael envelope of the smash product A#H in terms of the Arens-Michael envelope of H and a certain completion of A. We also give an example (Manin's quantum plane) showing that the result fails for non-Hopf bialgebras. ...

Added: March 12, 2013

191574970, Functional Analysis and Its Applications 1995 Vol. 29 No. 4 P. 276-279

Added: September 23, 2016

Akbarov S. S., Journal of Mathematical Sciences 2017 Vol. 227 No. 5 P. 531-668

Added: October 21, 2018

191574970, Mathematical notes 1995 Vol. 57 No. 3 P. 319-322

Added: September 23, 2016

Chmutov S., Kazaryan M., Lando S., Selecta Mathematica, New Series 2020 Vol. 26 No. 3 P. 1-22

We prove that the generating function for the symmetric chromatic polynomial of all simple graphs is (after an appropriate scaling change of variables) a linear combination of one-part Schur polynomials. This statement immediately implies that it is also a tau-function of the Kadomtsev–Petviashvili integrable hierarchy of mathematical physics. Moreover, we describe a large family of ...

Added: June 9, 2020