arXiv subjects

Ha Van Hieu

Publications and source records attributed to Ha Van Hieu.

3 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↗

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↗

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↗