scholarly journals Infinitesimal Deformations of the Model Z3-Filiform Lie Algebra

2013 ◽  
Vol 07 (01) ◽  
Keyword(s):  
Lie Algebra ◽  
Infinitesimal Deformations ◽  
Filiform Lie Algebra

scholarly journals Cohomology and deformations of the infinite-dimensional filiform Lie algebra m0

2007 ◽  
Vol 318 (2) ◽  
pp. 1002-1026 ◽  
Author(s):  
Alice Fialowski ◽  
Friedrich Wagemann
Keyword(s):  
Lie Algebra ◽  
Infinite Dimensional ◽  
Filiform Lie Algebra

scholarly journals Some Features of Rank One Real Solvable Cohomologically Rigid Lie Algebras with a Nilradical Contracting onto the Model Filiform Lie Algebra Qn

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 10 ◽  
Author(s):  
Rutwig Campoamor-Stursberg ◽  
Francisco Oviaño García
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Maximal Torus ◽  
Real Rank ◽  
Eigenvalue Spectrum ◽  
Generic Structure ◽  
Cohomology Space ◽  
Solvable Lie Algebras ◽  
Rank One ◽  
Filiform Lie Algebra

The generic structure and some peculiarities of real rank one solvable Lie algebras possessing a maximal torus of derivations with the eigenvalue spectrum spec ( t ) = 1 , k , k + 1 , ⋯ , n + k − 3 , n + 2 k − 3 for k ≥ 2 are analyzed, with special emphasis on the resulting Lie algebras for which the second Chevalley cohomology space vanishes. From the detailed inspection of the values k ≤ 5 , some series of cohomologically rigid algebras for arbitrary values of k are determined.

Some properties of a filiform Lie algebra

2020 ◽  
Vol 2020 (2) ◽  
pp. 164-170
Author(s):  
G.O. Solijanova
Keyword(s):  
Lie Algebra ◽  
Filiform Lie Algebra

scholarly journals FILIFORM LIE ALGEBRAS OF DIMENSION 8 AS DEGENERATIONS

2014 ◽  
Vol 13 (04) ◽  
pp. 1350144 ◽  
Author(s):  
JOAN FELIPE HERRERA-GRANADA ◽  
PAULO TIRAO
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Nilpotent Lie Algebras ◽  
Filiform Lie Algebras ◽  
Filiform Lie Algebra

For each complex 8-dimensional filiform Lie algebra we find another nonisomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of rank ≥ 1, only the characteristically nilpotent ones should be considered.

REPRESENTING FILIFORM LIE ALGEBRAS MINIMALLY AND FAITHFULLY BY STRICTLY UPPER-TRIANGULAR MATRICES

2013 ◽  
Vol 12 (04) ◽  
pp. 1250196 ◽  
Author(s):  
MANUEL CEBALLOS ◽  
JUAN NÚÑEZ ◽  
ÁNGEL F. TENORIO
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Nilpotent Lie Algebra ◽  
Algebra Isomorphism ◽  
Triangular Matrices ◽  
Nilpotent Lie Algebras ◽  
Upper Triangular Matrices ◽  
Filiform Lie Algebras ◽  
Filiform Lie Algebra

In this paper, we compute minimal faithful representations of filiform Lie algebras by means of strictly upper-triangular matrices. To obtain such representations, we use nilpotent Lie algebras [Formula: see text]n, of n × n strictly upper-triangular matrices, because any given (filiform) nilpotent Lie algebra [Formula: see text] admits a Lie-algebra isomorphism with a subalgebra of [Formula: see text]n for some n ∈ ℕ\{1}. In this sense, we search for the lowest natural integer n such that the Lie algebra [Formula: see text]n contains the filiform Lie algebra [Formula: see text] as a subalgebra. Additionally, we give a representative of each representation.

ON ISOMORPHISM CRITERIA FOR LEIBNIZ CENTRAL EXTENSIONS OF A LINEAR DEFORMATION OF μn

2011 ◽  
Vol 21 (05) ◽  
pp. 715-729 ◽  
Author(s):  
ISAMIDDIN S. RAKHIMOV ◽  
MUNTHER A. HASSAN
Keyword(s):  
Lie Algebra ◽  
Classification Problems ◽  
Linear Deformation ◽  
Central Extensions ◽  
Leibniz Algebras ◽  
Filiform Lie Algebra

This paper deals with the classification problems of Leibniz central extensions of linear deformations of a Lie algebra. It is known that any n-dimensional filiform Lie algebra can be represented as a linear deformation of n-dimensional filiform Lie algebra μn given by the brackets [ei, e0] = ei+1, i = 0,1,…,n - 2, in a basis {e0, e1,…,en - 1}. In this paper we consider a linear deformation of μn and its Leibniz central extensions. The resulting algebras are Leibniz algebras, this class is denoted here by Ced (μn). We choose an appropriate basis of Ced (μn) and give general isomorphism criteria. By using the isomorphism criteria, one can classify the class Ced (μn) for any fixed n. Two relevant maple programs are provided.

scholarly journals On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard Filiform Lie Algebra

CAUCHY ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 84
Author(s):  
Edi Kurniadi
Keyword(s):  
Lie Algebra ◽  
Lie Group ◽  
Unitary Representations ◽  
Identity Operator ◽  
Orbit Method ◽  
Irreducible Unitary Representations ◽  
Dimension 2 ◽  
Filiform Lie Group ◽  
Filiform Lie Algebra

<p class="Abstract">In this paper, we study irreducible unitary representations of a real standard filiform Lie group with dimension equals 4 with respect to its basis. To find this representations we apply the orbit method introduced by Kirillov. The corresponding orbit of this representation is genereric orbits of dimension 2. Furthermore, we show that obtained representation of this group is square-integrable. Moreover, in such case , we shall consider its Duflo-Moore operator as multiple of scalar  identity operator. In our case  that scalar is equal to one.</p>

scholarly journals Generalized Reynolds operators on 3-Lie algebras and NS-3-Lie algebras

2021 ◽  
Author(s):  
Shuai Hou ◽  
Yunhe Sheng
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Cohomology Group ◽  
Algebra Structure ◽  
Algebraic Structures ◽  
Reynolds Operator ◽  
Infinitesimal Deformations ◽  
Special Case

In this paper, first, we introduce the notion of a generalized Reynolds operator on a [Formula: see text]-Lie algebra [Formula: see text] with a representation on [Formula: see text]. We show that a generalized Reynolds operator induces a 3-Lie algebra structure on [Formula: see text], which represents on [Formula: see text]. By this fact, we define the cohomology of a generalized Reynolds operator and study infinitesimal deformations of a generalized Reynolds operator using the second cohomology group. Then we introduce the notion of an NS-[Formula: see text]-Lie algebra, which produces a 3-Lie algebra with a representation on itself. We show that a generalized Reynolds operator induces an NS-[Formula: see text]-Lie algebra naturally. Thus NS-[Formula: see text]-Lie algebras can be viewed as the underlying algebraic structures of generalized Reynolds operators on [Formula: see text]-Lie algebras. Finally, we show that a Nijenhuis operator on a 3-Lie algebra gives rise to a representation of the deformed 3-Lie algebra and a 2-cocycle. Consequently, the identity map will be a generalized Reynolds operator on the deformed 3-Lie algebra. We also introduce the notion of a Reynolds operator on a [Formula: see text]-Lie algebra, which can serve as a special case of generalized Reynolds operators on 3-Lie algebras.

scholarly journals Representasi Unitar Tak Tereduksi Grup Lie Dari Aljabar Lie Filiform Real Berdimensi 5

2020 ◽  
Vol 17 (1) ◽  
pp. 100-108
Author(s):  
E Kurniadi
Keyword(s):  
Harmonic Analysis ◽  
Lie Algebra ◽  
Unitary Representation ◽  
Lie Group ◽  
Dual Space ◽  
Irreducible Unitary Representation ◽  
Coadjoint Orbits ◽  
Dimensional Representation ◽  
Induced Representation ◽  
Filiform Lie Algebra

In this paper, we study a harmonic analysis of a Lie group  of a real filiform Lie algebra of dimension 5. Particularly, we study its  irreducible unitary representation (IUR) and contruct this IUR corresponds to its coadjoint orbits through coadjoint actions of its group to its dual space.  Using induced representation of  a 1-dimensional representation of its subgroup we obtain its IUR of its Lie group

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