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

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

On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard 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>

A distinguished example of filiform deformation

We exhibit the first example of a non-rigid complex filiform Lie algebra with all its codimension 1 ideals being characteristically nilpotent by constructing an explicit nontrivial filiform deformation of it.

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

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.

On isomorphism criterion for a subclass of complex filiform Leibniz algebras

In this paper, we present an algorithm to give the isomorphism criterion for a subclass of complex filiform Leibniz algebras arising from naturally graded filiform Lie algebras. This subclass appeared as a Leibniz central extension of a linear deformation of filiform Lie algebra. We give the table of multiplication choosing appropriate adapted basis, identify the elementary base changes and describe the behavior of structure constants under these base changes, then combining them the isomorphism criterion is given. The final result of calculations for one particular case also is provided.

FILIFORM LIE ALGEBRAS OF DIMENSION 8 AS DEGENERATIONS

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

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.