# Lie Algebras and Applications

@inproceedings{Iachello2006LieAA, title={Lie Algebras and Applications}, author={Francesco Iachello}, year={2006} }

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.

## 163 Citations

### CONTRACTIONS OF EXCEPTIONAL LIE ALGEBRAS AND SEMIDIRECT PRODUCTS

- Mathematics
- 2009

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

- Mathematics
- 2019

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

- Mathematics
- 2009

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

- MathematicsInt. J. Comput. Math.
- 2011

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

- Mathematics
- 2018

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

- Mathematics
- 2015

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

- Mathematics
- 2013

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

- MathematicsCommunications 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

- Mathematics
- 2010

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

- Mathematics
- 2010

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