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## On the equations defining affine algebraic groups

Pacific Journal of Mathematics. 2015. Vol. 279. No. 1--2 (Special issue In memoriam: Robert Steinberg). P. 423–446.

For the coordinate algebras of connected affine algebraic groups, we explore

the problem of finding a presentation by generators and relations canonically

determined by the group structure.

Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2015. No. 1508.02860.

For the coordinate algebras of connected affine algebraic groups, we explore the problem of finding a presentation by generators and relations canonically determined by the group structure. ...

Added: August 13, 2015

Vladimir L. Popov, Documenta Mathematica 2015 Vol. Extra Volume: Merkurjev's Sixtieth Birthday P. 513–528

A “rational” version of the strengthened form of the Commuting Derivation Conjecture, in which the assumption of commutativity
is dropped, is proved. A systematic method of constructing in any dimension greater than 3 the examples answering in the negative a question by M. El Kahoui is developed. ...

Added: September 25, 2015

Roman Avdeev, Petukhov A., Transformation Groups 2021 Vol. 26 No. 3 P. 719–774

Let G be a symplectic or special orthogonal group, let H be a connected reductive subgroup of G, and let X be a flag variety of G. We classify all triples (G, H, X) such that the natural action of H on X is spherical. For each of these triples, we determine the restrictions to ...

Added: September 2, 2020

Roman Avdeev, Selecta Mathematica, New Series 2015 Vol. 21 No. 3 P. 931–993

A subgroup H of an algebraic group G is said to be strongly solvable if H is contained in a Borel subgroup of G. This paper is devoted to establishing relationships between the following three combinatorial classifications of strongly solvable spherical subgroups in reductive complex algebraic groups: Luna’s general classification of arbitrary spherical subgroups restricted ...

Added: July 8, 2015

V. L. Popov, Proceedings of the Steklov Institute of Mathematics 2015 Vol. 290 P. 84–90

For every pair (G, V ) where G is a connected simple linear algebraic group and V is a simple algebraic G-module with a free algebra of invariants, the number of irreducible components of the nullcone of unstable vectors in V is found. ...

Added: September 25, 2015

Vladimir L. Popov, Proceedings of the Steklov Institute of Mathematics 2016 Vol. 292 P. 209–223

For every algebraically closed field k of characteristic different from 2, we prove
the following: (1) Finite-dimensional (not necessarily associative) k-algebras of general type
of a fixed dimension, considered up to isomorphism, are parametrized by the values of a tuple
of algebraically independent (over k) rational functions of the structure constants. (2) There
exists an “algebraic normal form” to ...

Added: March 29, 2016

Popov V. L., Mathematical notes 2019 Vol. 105 No. 3-4 P. 580–581

It is shown that the main result of N. R. Wallach, Principal orbit type theorems for reductive algebraic group actions and the Kempf–Ness Theorem, arXiv:1811.07195v1 (17 Nov 2018), is a special case of a more general statement, which can be deduced, using a short argument, from the classical Richardson and Luna theorems. ...

Added: May 27, 2019

V. L. Popov, Proceedings of the Steklov Institute of Mathematics, Springer 2019 Vol. 307 P. 193–197

We prove that, for any prime integer $p\geqslant 2$, there exists an algebraic action of the two-dimensional Witt group $W_2(p)$ on an al\-geb\-raic variety $X$ and a point $x\in X$ such that the closure of the $W_2(p)$-orbit of $x$
in $X$ contains infinitely many $W_2(p)$-orbits.\;This is related to the problem of extending from characteristic zero to ...

Added: March 30, 2020

Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2018. No. 1804.00323v1.

We prove that the family of all connected n-dimensional real Lie groups is uniformly Jordan for every n. This implies that all algebraic groups (not necessarily affine) over fields of cha\-racte\-ristic zero and some transformation groups of complex spaces and Riemannian manifods are Jordan. ...

Added: April 3, 2018

Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2015. No. 1503.08303.

For every pair (G, V ) where G is a connected simple
linear algebraic group and V is a simple algebraic G-module with
a free algebra of invariants, the number of irreducible components
of the nullcone of unstable vectors in V is found. ...

Added: March 31, 2015

Р.С. Авдеев, Горфинкель Н. Е., Функциональный анализ и его приложения 2012 Т. 46 № 3 С. 1–15

For all spherical homogeneous spaces G/H, where G is a simply connected semisimple algebraic group and H a connected solvable subgroup of G, we compute the spectra of representations of G on spaces of regular sections of homogeneous line bundles over G/H. ...

Added: February 25, 2014

Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2017. No. arXiv:1707.07720v1 [math.RT] 24 Jul 2017.

We first establish several general properties of modality of al gebraic group actions. In particular, we introduce the notion of a modali ty-regular action and prove that every visible action is modality-regular.
Then, using these results, we classify irreducible linear representations of
connected simple algebraic groups of every fixed modality < 3. Next, ex ploring a finer geometric structure of ...

Added: July 26, 2017

Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2014. No. 1401.0278.

We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results obtained are given. ...

Added: January 3, 2014

Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2022. No. 2206.14040.

We prove that every orbit of the adjoint representation of any connected reductive algebraic group G is a rational algebraic variety. For complex simply connected semisimple G, this implies rationality of affine Hamiltonian G-varieties (which we classify). ...

Added: June 29, 2022

V. L. Popov, Doklady Mathematics 2017 Vol. 96 No. 1 P. 312–314

For connected simple algebraic groups defined over an algebraically closed field of characteristic
zero, the classifications of irreducible algebraic representations of modalities 0, 1, and 2 are obtained. ...

Added: June 30, 2017

Arzhantsev I., Communications in Algebra 2008 Vol. 36 No. 12 P. 4368–4374

Added: July 10, 2014

Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2014. No. 1409.6330.

A "rational" version of the strengthened form of the Commuting Derivation Conjecture, in which the assumption of commutativity is dropped, is proved. A systematic method of constructing in any dimension greater than 3 the examples answering in the negative a question by M. El Kahoui is developed. ...

Added: September 24, 2014

Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2017. No. 1707.06914 [math.AG].

We classify all connected affine algebraic groups G such that there are only finitely many G-orbits in every algebraic G-variety containing a dense open G-orbit. We also prove that G enjoys this property if and only if every irreducible algebraic G-variety X is modality-regular, i.e., the modality of X (in the sense of V. Arnol’d) ...

Added: July 24, 2017

Kham T., Социальные и гуманитарные науки: теория и практика 2019 № 1(3) С. 167–183

The article examines the problems of defining the term computer simulations of scientific experiments. The first part analyzes the original method for classifying variations of terms proposed by Duran as the most successful for demonstrating significant existing contradictions among philosophers regarding the place and role of computer simulations in the philosophy of science. In the ...

Added: December 11, 2019

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

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