arXiv subjects

Le Anh Vu

Publications and source records attributed to Le Anh Vu.

12 recordsLinked to original sources

arXiv2020

Some Applications of Lie Groups in Theory of Technical Progress

In recent decades, we have known some interesting applications of Lie theory in the theory of technological progress. Firstly, we will discuss some results of R. Saito in \cite{rS1980} and \cite{rS1981} about the application modeling of Lie groups in the theory of technical progress. Next, we will describe the result on Romanian economy of G. Zaman and Z. Goschin in \cite{ZG2010}. Finally, by using Sato's results and applying the method of G. Zaman and Z. Goschin, we give an estimation of the GDP function of Viet Nam for the 1995-2018 period and give several important observations about the impact of technical progress on economic growth of Viet Nam.

q-fin.GN↗

arXiv2019

Cohomology of some families of Lie algebras and quadratic Lie algebras

The paper studies the cohomology of Lie algebras and quadratic Lie algebras. Firstly, we propose to describe the cohomology of $MD(n,1)$-class which was introduced in \cite{LHNCN16}. This class contains Heisenberg Lie algebras. In 1983, L. J. Santharoubane \cite{San83} computed the cohomology of Heisenberg Lie algebras. In this paper, we will completely describe the cohomology of the other ones of $MD(n, 1)$-class. Finally, we will be concerned about the cohomology of quadratic Lie algebras. In 1985, A. Medina and P. Revoy \cite{MR85} computed the second Betti number of the generalized real diamond Lie algebras. We will compute in this paper the second Betti number of the generalized complex diamond Lie algebras by using the super-Poisson bracket.

math.RA↗

arXiv2017

The Second Cohomology Group of Elementary Quadratic Lie Superalgebras and Classifying a Subclass of 8-dimensional Solvable Quadratic Lie Superalgebras

By definition, a quadratic Lie superalgebra is a Lie superalgebra endowed with a non-degenerate supersymmetric bilinear form which satisfies the even and invariant properties. In this paper we calculate all of the second cohomology group of elementary quadratic Lie superalgebras which have been classified in \cite{DU14} by applying the super-Poisson bracket on the super exterior algebra. Besides, we give the classification of 8-dimensional solvable quadratic Lie superalgebras having 6-dimensional indecomposable even part. The method is based on the double extension and classification results of adjoint orbits of the Lie algebra $\mathfrak{s}\mathfrak{p}(2)$.

math.RA↗

arXiv2015

Classification of Real Solvable Lie Algebras Whose Simply Connected Lie Groups Have Only Zero or Maximal Dimensional Coadjoint Orbits

In this paper we study a special subclass of real solvable Lie algebras having small dimensional or small codimensional derived ideal. It is well-known that the derived ideal of any Heisenberg Lie algebra is 1-dimensional and the derived ideal of the 4-dimensional real Diamond algebra is 1-codimensional. Moreover, all the coadjoint orbits of any Heisenberg Lie group as well as 4-dimensional real Diamond group are orbits of dimension zero or maximal dimension. In general, a (finite dimensional) real solvable Lie group is called an $MD$-group if its coadjoint orbits are zero-dimensional or maximal dimensional. The Lie algebra of an $MD$-group is called an $MD$-algebra and the class of all $MD$-algebras is called $MD$-class. Simulating the mentioned above characteristic of Heisenberg Lie algebras and 4-dimensional real Diamond algebra, we give a complete classification of $MD$-algebras having 1-dimensional or 1-codimensional derived ideals.

math.RA↗

arXiv2014

K-theory for the Leaf Spaces of the Orbit Foliations of the co-adjoint Action of some 5-dimensional Solvable Lie groups

In this paper, combining Kirillov's method of orbits with Connes' method in Differential Geometry, we study the so-called MD(5,3C)-foliations, i.e. the orbit foliations of the co-adjoint action of MD(5,3C)-groups. First, we classify topologically MD(5,3C)-foliations based on the classification of all MD(5,3C)-algebras in [22] and the picture of co-adjoint orbits (K-orbits) of all MD(5,3C)-groups in [23]. Finally, we study K-theory for leaf space of MD(5,3C)-foliations and describe analytically or characterize Connes' C*-algebras of the considered foliations by KK-functors.

math.KT↗

arXiv2014

K-theory for the Leaf Space of Foliations Formed by the Generic K-orbits of a class of Solvable Real Lie Groups

The paper is a continuation of the works [17] of Vu and Shum, [18] and [19] of Vu and Hoa. In [17], Vu and Shum classified all the MD5-algebras having commutative derived ideals. In [18], Vu and Hoa considered foliations formed by the maximal dimensional K-orbits (for short, MD5-foliations) of connected MD5-groups such that their Lie algebras have 4-dimensional commutative derived ideals and gave a topological classification of the considered foliations. In [19], Vu and Hoa characterized the Connes' C*-algebras of some MD5-foliations considered in \cite{VU-HO09} by the method of K-functors. In this paper, we study K-theory for the leaf space of all MD5-foliations which are classified in [18] and characterize the Connes' C*-algebras of them by the method of K-functors.

math.KT↗

arXiv2012

Classification of 5-Dimensional MD-Algebras Having Non-Commutative Derived Ideals

The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e. five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbits) are orbits of zero or maximal dimension. The main result of the paper is the classification up to an isomorphism of all MD5-algebras with the non-commutative derived ideal. With this result, we have the complete classification of 5-dimensional solvable Lie algebras.

math.RT↗

arXiv2011

K-Theory for the Leaf Space of Foliations formed by the Generic K-Ornits of some indecomposable $MD_5$-Groups

The paper is a continuation of the authors' work in which we considered foliations formed by the maximal dimensional K-orbits ($MD_5$-foliations) of connected $MD_5$-groups such that their Lie algebras have 4-dimensional commutative derived ideals and give the topological classification of considered foliations. In this paper, we study K-theory for the leaf space of some from these $MD_5$-foliations and analytically describes and characterized Connes' C*-algebras of considered foliations by the method of K-functors.

math.KT↗

arXiv2008

The Topology of Foliations Formed by the Generic K-Orbits of a Subclass of the Indecomposable MD5-Groups

The present paper is a continuation of [13], [14] of the authors. Specifically, the paper considers the MD5-foliations associated to connected and simply connected MD5-groups such that their Lie algebras have 4-dimensional commutative derived ideal. In the paper, we give the topological classification of all considered MD5-foliations. A description of these foliations by certain fibrations or suitable actions of $\mathbb{R}^{2}$ and the Connes' C*-algebras of the foliations which come from fibrations are also given in the paper.

math.DG↗

arXiv2008

Classification of 5-dimensional MD-algebras having commutive derived ideals

In this paper, we study a subclass of the class of MD-algebras, i.e., the class of solvable real Lie algebras such that the K-orbits of its corresponding connected and simply connected Lie groups are either orbits of dimension zero or orbits with maximal dimensions. Our main result is to classify, up to isomorphism, all the 5-dimensional MD-algebras having commutative derived ideals.

math.RA↗

arXiv2006

On a Subclass of 5-Dimensional Solvable Lie Algebras Which Have 3-Dimensional Commutative Derived Ideal

The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e., five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbit) are orbit of zero or maximal dimension. The main results of the paper is the classification up to an isomorphism of all MD5-algebras $\mathcal{G}$ with the derived ideal ${\mathcal{G}}^{1} := [\mathcal{G}, \mathcal{G}]$ is a 3-dimensional commutative Lie algebra.

math.RT↗

arXiv2006

The Geometry of K-Orbits of a Subclass of MD5-Groups and Foliations Formed by their Generic K-Orbits

The present paper is a continuation of Le Anh Vu's ones [13], [14], [15]. Specifically, the paper is concerned with the subclass of connected and simply connected MD5-groups such that their MD5-algebras $\mathcal{G}$ have the derived ideal ${\mathcal{G}}^{1} : = [ \mathcal{G},\mathcal{G} ]\equiv$ ${\bf{R}}^{3}$. We shall describe the geometry of K-orbits of these MD5-groups. The foliations formed by K-orbits of maximal dimension of these MD5-groups and their measurability are also presented in the paper.

math.DG↗