English
Related papers

Related papers: A class of Solvable Lie algebras

200 papers

The filiform and the quasi-filiform Lie algebras form a special class of nilpotent Lie algebras. The aim of this paper is to compute the index and provide regular vectors of this two class of nilpotent Lie algebras. we consider the graded…

Representation Theory · Mathematics 2012-12-10 Hadjer Adimi , Abdenacer Makhlouf

Denote m_0 the infinite dimensional N-graded Lie algebra defined by basis e_i, i>= 1 and relations [e_1,e_i] = e_(i+1) for all i>=2. We compute in this article the bracket structure on H1(m_0,m_0), H2(m_0,m_0) and in relation to this, we…

Representation Theory · Mathematics 2011-11-09 Alice Fialowski , Friedrich Wagemann

The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded quasi-filiform algebra and the complemented space to the…

Rings and Algebras · Mathematics 2021-05-28 K. K. Abdurasulovand , J. Q. Adashev

In this paper, we are interested in solvable complete Lie algebras, over the field $\K=\R$ or $\mathbb{C}$, which admit a symplectic structure. Specifically, important classes are studied, and a description of complete Lie Algebra with the…

Differential Geometry · Mathematics 2024-07-01 M. Benyoussef , M. W. Mansouri , SM. Sbai

The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded $p$-filiform non-Lie Leibniz algebra $(n-p\geq4)$ and the…

Rings and Algebras · Mathematics 2019-02-13 J. Q. Adashev , L. M. Camacho , B. A. Omirov

For a natural number $m$, a Lie algebra $L$ over a field $k$ is said to be of breadth type $(0, m)$ if the co-dimension of the centralizer of every non-central element is of dimension $m$. In this article, we classify finite dimensional…

Rings and Algebras · Mathematics 2024-04-04 Rijubrata Kundu , Tushar Kanta Naik , Anupam Singh

Leibniz superalgebras with nilindex $n + m$ and characteristic sequence $(n-1, 1 \ | \ m)$ divided into four parametric classes that contain a set of non-isomorphic superalgebras. In this paper, we give a complete classification of solvable…

Rings and Algebras · Mathematics 2024-02-14 Khudoyberdiyev A. Kh. , Muratova Kh. A

The paper is devoted to give a full classification of all finite dimensional nilpotent Lie algebras $ L $ of class $4$ such that $ \dim L^2=3. $ Moreover, we classify the capable ones.

Rings and Algebras · Mathematics 2021-05-21 Faangis Johari , Peyman Niroomand , Mohsen Parvizi

We extend the classification of solvable Lie algebras with abelian nilradicals to classify solvable Leibniz algebras which are one dimensional extensions of an abelian nilradicals.

Rings and Algebras · Mathematics 2014-10-02 Lindsey Bosko-Dunbar , Matthew Burke , Jonathan D. Dunbar , J. T. Hird , Kristen Stagg Rovira

In this paper we give the classification of the irreducible non solvable Lie algebras of dimensions $\leq 13$ with nondegenerate, symmetric and invariant bilinear forms.

Rings and Algebras · Mathematics 2015-06-19 Said Benayadi , Alberto Elduque

In this paper, we classify solvable quadratic Lie algebras up to dimension 6. In dimensions smaller than 6, we use the Witt decomposition given in \cite{Bou59} and a result in \cite{PU07} to obtain two non-Abelian indecomposable solvable…

Rings and Algebras · Mathematics 2012-04-24 Tien Dat Pham , Anh Vu Le , Minh Thanh Duong

We extend the classical construction of solvable Lie algebras from a nilradical to compatible Lie algebras. Since the sum of nilpotent ideals may fail to be nilpotent, we replace the usual nilradical by a \emph{special nilradical} that…

Rings and Algebras · Mathematics 2026-03-02 A. Fernández Ouaridi , R. M. Navarro , B. A. Omirov , G. O. Solijanova

For a finite dimensional Lie algebra $L$, it is known that $s(L)=\f{1}{2}(n-1)(n-2)+1-\mathrm{dim} M(L)$ is non negative. Moreover, the structure of all finite nilpotent Lie algebras is characterized when $s(L)=0,1$ in \cite{ni,ni4}. In…

Rings and Algebras · Mathematics 2021-05-21 Peyman Niroomand

In this paper solvable Leibniz algebras with naturally graded non-Lie $p$-filiform $(n-p\geq4)$ nilradical and with one-dimensional complemented space of nilradical are described. Moreover, solvable Leibniz algebras with abelian nilradical…

Rings and Algebras · Mathematics 2016-05-04 J. Q. Adashev , M. Ladra , B. A. Omirov

In this paper we show that the method for describing solvable Lie algebras with given nilradical by means of non-nilpotent outer derivations of the nilradical is also applicable to the case of Leibniz algebras. Using this method we extend…

Rings and Algebras · Mathematics 2012-03-22 J. M. Casas , M. Ladra , B. A. Omirov , I. A. Karimjanov

In math.DG/0312243 we developed a general classification scheme for metric Lie algebras, i.e. for finite-dimensional Lie algebras equipped with a non-degenerate invariant inner product. Here we determine all nilpotent Lie algebras l with…

Differential Geometry · Mathematics 2014-02-28 Ines Kath

This article can be viewed as a continuation of the articles arXiv:0912.3486 and arXiv:1012.3714 where the decomposable Lie algebras admitting half-flat SU(3)-structures are classified. The new main result is the classification of the…

Differential Geometry · Mathematics 2013-02-06 Marco Freibert , Fabian Schulte-Hengesbach

This paper is devoted to the characterization of all finite dimensional nilpotent Lie algebras $L$ with $S^{2}(L)=0,1,2,3$, where we define $dim ~\mathcal{M}^{2}(L) = \dfrac{1}{3}n(n-1)(n-2)+3-S^{2}(L).$

Rings and Algebras · Mathematics 2018-12-04 Rudra Narayan Padhan , K. C. Pati

We present a list of all isomorphism classes of nonsolvable Lie algebras of dimension less than 7 over a finite field.

Rings and Algebras · Mathematics 2007-05-23 Helmut Strade

This paper presents a classification of 7-dimensional real and complex indecomposable solvable Lie algebras having some 5-dimensional nilradicals. Afterwards, we combine our results with those of Rubin and Winternitz (1993), Ndogmo and…

Rings and Algebras · Mathematics 2021-07-09 Vu A. Le , Tuan A. Nguyen , Tu T. C. Nguyen , Tuyen T. M. Nguyen , Thieu N. Vo