scholarly journals Weight multiplicity formulas for bivariate representations of classical Lie algebras

2018 ◽  
Vol 59 (8) ◽  
pp. 081705 ◽  
Author(s):  
Emilio A. Lauret ◽  
Fiorela Rossi Bertone
Keyword(s):  
Lie Algebras ◽  
Weight Multiplicity

scholarly journals When is the $q$-Multiplicity of a Weight a Power of $q$?

10.37236/8758 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Pamela E. Harris ◽  
Margaret Rahmoeller ◽  
Lisa Schneider ◽  
Anthony Simpson
Keyword(s):  
Lie Algebras ◽  
Dynkin Diagram ◽  
Fibonacci Numbers ◽  
Simple Lie Algebras ◽  
Weight Multiplicity ◽  
Highest Weight ◽  
Multiplicity Formula ◽  
Exhaustive List

Berenshtein and Zelevinskii provided an exhaustive list of pairs of weights $(\lambda,\mu)$ of simple Lie algebras $\mathfrak{g}$ (up to Dynkin diagram isomorphism) for which the multiplicity of the weight $\mu$ in the representation of $\mathfrak{g}$ with highest weight $\lambda$ is equal to one. Using Kostant's weight multiplicity formula we describe and enumerate the contributing terms to the multiplicity for subsets of these pairs of weights and show that, in these cases, the cardinality of these contributing sets is enumerated by (multiples of) Fibonacci numbers. We conclude by using these results to compute the associated $q$-multiplicity for the pairs of weights considered, and conjecture that in all cases the $q$-multiplicity of such pairs of weights is given by a power of $q$.

The rigidity of some solvable Lie algebras

2018 ◽  
Vol 2018 (2) ◽  
pp. 43-49
Author(s):  
R.K. Gaybullaev ◽  
Kh.A. Khalkulova ◽  
J.Q. Adashev
Keyword(s):  
Lie Algebras ◽  
Solvable Lie Algebras

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

2018 ◽  
Vol 13 (3) ◽  
pp. 59-63 ◽  
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Gas Dynamics ◽  
Hydrodynamic Type ◽  
System Of Equations ◽  
Two Dimensional ◽  
Equations Of Gas Dynamics ◽  
Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

scholarly journals Abelian extensions and crossed modules of Hom-Lie algebras

2020 ◽  
Vol 224 (3) ◽  
pp. 987-1008
Author(s):  
José Manuel Casas ◽  
Xabier García-Martínez
Keyword(s):  
Lie Algebras ◽  
Abelian Extensions ◽  
Crossed Modules

On parakähler Hom-Lie algebras and Hom-left-symmetric bialgebras

2016 ◽  
Vol 45 (1) ◽  
pp. 105-120 ◽  
Author(s):  
Qinxiu Sun ◽  
Hongliang Li
Keyword(s):  
Lie Algebras

Lie algebras graded by the weight system (Θ ,sl)

2021 ◽  
Vol 581 ◽  
pp. 1-44
Author(s):  
Alexander Baranov ◽  
Hogir M. Yaseen
Keyword(s):  
Lie Algebras ◽  
Weight System
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