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## On continuous duality for Moore groups

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 a narrower class of groups of the form R^n × K × D, where K is a compact group and D a discrete Moore group. In this paper we correct the errors of Kuznetsova’s work and prove the validity (up to some speciﬁcations in terminology) of her theory for all Moore groups.

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

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

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

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., 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, 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

Akbarov S. S., Mathematical notes 2018 Vol. 104 No. 3 P. 465-468

In [1] and [3], the author described the stereotype approximation property, which is an analog of the classical approximation property transferred to the category Ste of stereotype spaces. It was noticed in [3] that, for a stereotype space X, the stereotype approximation condition is formally stronger than the classical approximation condition (although, up to now, ...

Added: October 21, 2018

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

Added: September 23, 2016

Румынин Д. А., Hristova K., Journal of Algebra 2018 Vol. 515 P. 202-235

We investigate smooth representations of complete Kac-Moody groups. We approach representation theory via geometry, in particular, the group action on the Davis realisation of its Bruhat-Tits building. Our results include an estimate on projective dimension, localisation theorem, unimodularity and homological duality. ...

Added: October 8, 2018

Smirnova N., Тарашнина С. И., Известия высших учебных заведений. Математика 2016 Т. 6 С. 63-74

As a solution concept of cooperative TU-game we propose the set of $\alpha$-prenucleoli, $\alpha\in R$, that is a generalization of the $[0,1]$-prenucleolus. In the paper we show that in a cooperative game the set of $\alpha$-prenucleoli takes into account the constructive power with weight $\alpha$ and the blocking power with weight $(1-\alpha)$ for all possible ...

Added: October 20, 2015

191574970, Nova Science Publishers, 2000

Added: September 23, 2016

191574970, IMPAN, 2005

Added: September 23, 2016

Dietzenbacher B., Estévez-Fernández A., Borm P. et al., Annals of Operations Research 2020

This paper studies bankruptcy problems with nontransferable utility as a generalization of bankruptcy problems with monetary estate and claims. Following the theory on TU-bankruptcy, we introduce a duality notion for NTU-bankruptcy rules and derive several axiomatic characterizations of the proportional rule and the constrained relative equal awards rule. ...

Added: June 2, 2020

Zatelepin A., Shchur L., Duality of critical interfaces in Potts model: numerical check / Cornell University. Series "Working papers by Cornell University". 2010. No. 1008.3573.

We report on numerical investigation of fractal properties of critical interfaces in two-dimensional Potts models. Algorithms for finding percolating interfaces of Fortuin-Kasteleyn clusters, their external perimeters and interfaces of spin clusters are presented. Fractal dimensions are measured and compared to exact theoretical predictions. ...

Added: March 7, 2016

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

Added: September 23, 2016

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

Added: September 23, 2016

Smirnova N., Tarashnina S. I., Russian Mathematics 2016 Vol. 60 No. 6 P. 63-74

We understand a solution of a cooperative TU-game as the α-prenucleoli set, α ∈ R, which is a generalization of the notion of the [0, 1]-prenucleolus. We show that the set of all α-nucleoli takes into account the constructive power with the weight α and the blocking power with the weight (1 − α) for all possible values of the parameter α. The ...

Added: July 7, 2016

Akbarov S. S., Математический сборник 2022 Т. 213 № 5 С. 3-29

We prove two identities that connect some natural tensor products in the category $\sf{LCS}$ of locally convex spaces with the tensor products in the category $\sf{Ste}$ of stereotype spaces. In particular, we give sufficient conditions under which the identity
$$
X^\vartriangle\odot Y^\vartriangle\cong (X^\vartriangle\cdot Y^\vartriangle)^\vartriangle\cong (X\cdot Y)^\vartriangle
$$
holds, where $\odot$ is the injective tensor product in the category $\sf{Ste}$,
$\cdot$, ...

Added: December 21, 2021

Feigin B. L., Jimbo M., Mukhin E., Communications in Mathematical Physics 2019 No. 367 P. 455-481

On a Fock space constructed from mn free bosons and lattice Z mn , we give a level n action of the quantum toroidal algebra E m associated to gl m , together with a level m action of the quantum toroidal algebra E n associated to gl n . We prove that the E ...

Added: December 10, 2019

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

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

Added: September 23, 2016

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

Added: September 23, 2016

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016