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## Группы базовых автоморфизмов картановых слоений моделируемых на неэффективных картановых геометриях.

Труды Математического центра им. Н.И. Лобачевского. 2015. Т. 52. С. 73-74.

Publication based on the results of:

Sheina K., Basic automorphism of Cartan foliations covered by fibrations / Cornell University. Series arXiv "math". 2020. No. 04348v1.

The basic automorphism group of a Cartan foliation (M, F) is the quotient group of the automorphism group of (M, F) by the normal subgroup, which preserves every leaf invariant. For Cartan foliations covered by fibrations, we find sufficient conditions for the existence of a structure of a finite-dimensional Lie group in their basic automorphism groups. Estimates ...

Added: December 9, 2020

Sheina K., Известия высших учебных заведений. Поволжский регион. Физико-математические науки 2021 Т. 1 № 1 С. 49-65

The basic automorphism group of a Cartan foliation (M,F) is the quotient group of the automorphism group of (M, F ) by the normal subgroup, which preserves every leaf invariant. For Cartan foliations covered by fibrations, we find sufficient conditions for the existence of a structure of a finite-dimensional Lie group in their basic automorphism ...

Added: December 16, 2020

Zhukova N.I., K. I. Sheina, Basic automorphism groups of complete Cartan foliations covered by fibrations / Cornell University. Series math "arxiv.org". 2015. No. 1410.1144 .

We get sufficient conditions for the full basic automorphism group of a complete
Cartan foliation to admit a unique (finite-dimensional) Lie group structure in the category
of Cartan foliations. In particular, we obtain sufficient conditions for this group
to be discrete. Emphasize that the transverse Cartan geometry may be noneffective.
Some estimates of the dimension of this group depending ...

Added: November 10, 2014

Basic automorphism groups of complete Cartan foliations covered by fibrations / Cornell University. Series arXiv "math". 2015. No. 1410.1144.

We get sufficient conditions for the full basic automorphism group of a complete Cartan foliation to admit a unique (finite-dimensional) Lie group structure in the category of Cartan foliations. In particular, we obtain sufficient conditions for this group to be discrete. Emphasize that the transverse Cartan geometry may be noneffective. Some estimates of the dimension ...

Added: September 28, 2015

Н.И. Жукова, Шеина К. И., Труды Математического центра им. Н.И. Лобачевского 2014 Т. 50 С. 74-76

We investigate Cartan foliations covered by fibrations. We obtain a sufficient condition for the full
basic automorphism group of a complete Cartan foliation covered by fibration to admit a
unique (finite-dimensional) Lie group structure in the category of
Cartan foliations. The explicit new formula for determining its basic automorphism
Lie group is given. Examples of computing the full basic ...

Added: November 12, 2014

K. I. Sheina, N. I. Zhukova, Lobachevskii Journal of Mathematics 2018 Vol. 39 No. 2 P. 271-280

For a complete Cartan foliation (M; F) we introduce
two algebraic invariants g0(M; F) and g1(M; F) which we call structure
Lie algebras. If the transverse Cartan geometry of (M; F) is eective
then g0(M; F) = g1(M; F). We prove that if g0(M; F) is zero then in
the category of Cartan foliations the group of all basic ...

Added: March 23, 2017

Shirokov D., Advances in Applied Clifford Algebras 2021 Vol. 31 Article 30

In this paper, we consider inner automorphisms that leave invariant fixed subspaces of real and complex Clifford algebras — subspaces of fixed grades and subspaces determined by the reversion and the grade involution. We present groups of elements that define such inner automorphisms and study their properties. Some of these Lie groups can be interpreted ...

Added: May 10, 2021

Shirokov D., Advances in Applied Clifford Algebras 2012 Vol. 22 No. 1 P. 243-256

We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method for analyzing commutators and anticommutators of Clifford algebra elements. This method allows us to find out and prove a number of new properties of Clifford algebra elements. ...

Added: June 16, 2015

Shirokov D., Advances in Applied Clifford Algebras 2010 Vol. 20 No. 2 P. 411-425

In this paper we present new formulas, which represent commutators and anticommutators of Clifford algebra elements as sums of elements of different ranks. Using these formulas we consider subalgebras of Lie algebras of pseudo-unitary groups. Our main techniques are Clifford algebras. We have found 12 types of subalgebras of Lie algebras of pseudo-unitary groups. ...

Added: June 16, 2015

Sheina K., Zhukova N., Lobachevskii Journal of Mathematics 2016

For a complete Cartan foliation $(M,F)$ we introduce two algebraic invariants $\frak{g}_{0}(M,F)$ and
${\frak g}_{1}(M,F)$ which we
call structure Lie
algebras. If the transverse Cartan geometry of $(M,F)$ is effective then
$\frak{g}_{0}(M,F)={\frak g}_{1}(M,F)$. We prove that if $\frak{g}_{0}(M,F)$
is zero then in the category of Cartan foliations the group of all basic automorphisms of the ...

Added: October 12, 2016

Bazaikin Y., Galaev A., Zhukova N., Chaos 2020 Vol. 30 P. 1-9

Chaotic foliations generalize Devaney's concept of chaos for
dynamical systems. The property of a foliation to
be chaotic is transversal. The existence problem of chaos for a Cartan foliation
is reduced to the corresponding problem for its holonomy pseudogroup of
local automorphisms of a transversal manifold. Chaotic foliations with transversal Cartan ...

Added: October 6, 2020

Shirokov D., Journal of Geometry and Symmetry in Physics 2016 Vol. 42 P. 73-94

In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove isomorphisms between these groups and classical matrix groups (symplectic, orthogonal, linear, unitary) in the cases of arbitrary dimension and arbitrary signature. Also we obtain isomorphisms of corresponding Lie algebras ...

Added: December 14, 2016

N. I. Zhukova, Journal of Mathematical Sciences 2016 Vol. 219 No. 1 P. 112-124

We consider a Cartan foliation (M,F) of an arbitrary codimension q admitting an
Ehresmann connection such that all leaves of (M,F) are embedded submanifolds of M.
We prove that for any foliation (M,F) there exists an open, not necessarily connected,
saturated, and everywhere dense subset M0 of M and a manifold L0 such that the induced
foliation (M0, FM0) ...

Added: October 21, 2016

Nina. I. Zhukova, Galaev A., Attractors of Cartan foliation / Cornell University. Series math "arxiv.org". 2017.

The paper is focused on the existence problem of attractors for foliations. Since the existence of an attractor is a transversal property of the foliation, it is natural to consider foliations admitting transversal geometric structures. As transversal structures are chosen Cartan geometries due to their universality. The existence problem of an attractor on a complete ...

Added: March 23, 2017

N. I. Zhukova, Journal of Geometry and Physics 2018 Vol. 132 P. 146-154

We present a new method of investigation of G-structures on orbifolds.
This method is founded on the consideration of a G-structure on an
n-dimensional orbifold as the corresponding transversal
structure of an associated foliation. Using this method we prove the
existence and the uniqueness of a finite dimensional Lie group structures
on the full automorphism group of an elliptic G-structure ...

Added: April 4, 2017

Zhukova N. I., Mathematical notes 2013 Vol. 93 No. 5-6 P. 928-931

In this paper a unified method for studying foliations with transversal parabolic geometry of rank one is presented.
Ideas of Fraces' paper on parabolic geometry of rank one and of works of the author on conformal foliations
are developed. ...

Added: October 19, 2014

V. L. Popov, Mathematical notes 2018 Vol. 103 No. 5 P. 811-819

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

Added: April 13, 2018

Popov V., Известия РАН. Серия математическая 2022 Т. 86 № 5 С. 73-96

We explore to what extent the group variety of a connected algebraic group or the group manifold of a real Lie group determines its group structure. ...

Added: June 9, 2022

Zhukova N., Уфимский математический журнал 2018 Т. 10 № 2 С. 43-56

The groups of conformal transformations of $n$-dimensional
pseudo-Riemannian orbifolds $({\mathcal N},g)$ are investigated for $n\geq 3$.
The Alekseevskii method of the investigation of the conformal transformation groups of
Riemannian manifolds is extended by us to psevdo-Riemannian orbifolds. It is shown that
a conformal pseudo-Riemannian geometry is induced on each stratum of that orbifold. Due to this,
for $k\in\{0,1\}\cup\{3,...,n-1\}$ exact estimates ...

Added: March 19, 2018

Vladimir L. Popov, The Jordan property for Lie groups and automorphism groups of complex spaces / 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

Kharchev S. M., Khoroshkin S. M., Advances in Mathematics 2020 Vol. 375 No. 107368 P. 1-56

We obtain certain Mellin-Barnes integrals which present Whittaker wave functions related to classical real split forms of simple complex Lie groups ...

Added: October 18, 2020

Vladimir L. Popov, Underlying varieties and group structures / Cornell University. Series math "arxiv.org". 2021. No. 2105.12861.

Starting with exploration of the possibility to present the underlying variety of an affine algebraic group in the form of a product of some algebraic varieties, we then explore the naturally arising problem as to what extent the group variety of an algebraic group determines its group structure. ...

Added: May 28, 2021

Н.И. Жукова, Mathematical Notes (Rusian Federation) 2013 Т. 93 № 6 С. 994-996

In this paper a unified method for studying foliations with transversal psrsbolic geometry of rank one is presented.
Ideas of Fraces' paper on parabolic geometry of rank one and of works of the author on conformal foliations
are developed. ...

Added: September 28, 2014

В. Л. Попов, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2021 Т. 500 № 1 С. 52-54

It is explored to which extent the group variety of an algebraic group determines its group structure. ...

Added: November 18, 2021