Lie Algebras and Applications

  title={Lie Algebras and Applications},
  author={Francesco Iachello},
Basic Concepts.- Semisimple Lie Algebras.- Lie Groups.- Lie Algebras and Lie Groups.- Homogeneous and Symmetric Spaces (Coset Spaces). - Irreducible Bases (Representations).- Casimir Operators and Their Eigenvalues.- Tensor Operators.- Boson Realizations.- Fermion Realizations.- Differential Realizations.- Matrix Realizations.- Coset Spaces.- Spectrum Generating Algebras and Dynamic Symmetries.- Degeneracy Algebras and Dynamical Alebras.- Index. 


For any semisimple subalgebra s′ of exceptional Lie algebras s satisfying the constraint rank(s′) = rank(s)−1 we analyze the branching rules for the adjoint representation, and determine the

Lie Groups, Lie Algebras and some applications in Physics

Given a Lie algebra g and its complexi cation gC, the representations of gC are isomorphic to those of g. Moreover, if g is the corresponding Lie algebra of a connected and simply connected Lie group

Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators

Given a semidirect product of semisimple Lie algebras and solvable algebras , we construct polynomial operators in the enveloping algebra of that commute with and transform like the generators of ,

Complete triangular structures and Lie algebras

The families of n-dimensional Lie algebras associated with a combinatorial structure made up of n vertices and with its edges forming a complete simple, undirected graph are studied.

Symmetry algebras of the canonical Lie group geodesic equations in dimension three

For each of the two and three-dimensional indecomposable Lie algebras the geodesic equations of the associated canonical Lie group connection are given. In each case a basis for the associated Lie

Abelian subalgebras on Lie algebras

Abelian subalgebras play an important role in the study of Lie algebras and their properties and structures. In this paper, the historical evolution of this concept is shown, analyzing the current

A note on semidirect sum of Lie algebras

In the paper there are investigated some properties of Lie algebras, the construction which has a wide range of applications like computer sciences (especially to computer visions), geometry or

Nilpotent decomposition of solvable Lie algebras

  • L. Qi
  • Mathematics
    Communications in Mathematical Sciences
  • 2020
Semisimple Lie algebras have been completely classified by Cartan and Killing. The Levi theorem states that every finite dimensional Lie algebra is isomorphic to a semidirect sum of its largest

Solvable Lie algebras with an -graded nilradical of maximal nilpotency degree and their invariants

The class of solvable Lie algebras with an -graded nilradical of maximal nilpotency index is classified. It is shown that such solvable extensions are unique up to isomorphism. The generalized

Contractions of Exceptional Lie Algebras and Semidirect Products

For any semisimple subalgebra s0 of exceptional Lie algebras s satisfying the constraint rank(s0) = rank(s)