We consider some unitary representations of infinite dimensional Lie algebras motivated by string theory on AdS3. These include examples of two kinds: the A,D,E type affine Lie algebras and the N = 4 superconformal algebra. The first presents a new construction for free field representations of affine Lie algebras. The second is of a particular physical interest because it provides some hints t...

We construct and study various dual pairs between finite dimensional classical Lie groups and infinite dimensional Lie algebras in some Fock representations. The infinite dimensional Lie algebras here can be either a completed infinite rank affine Lie algebra, the W1+∞ algebra or its certain Lie subalgebras. We give a formulation in the framework of vertex algebras. We also formulate several co...

This paper presents an overview of the representations of Lie algebras, particularly semi-simple Lie algebras, with a view towards theoretical physics. We proceed from the relationship between Lie algebras and Lie groups to more abstract characterizations of Lie groups, give basic definitions of different properties that may characterize Lie groups, and then prove results about root systems, pr...

Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of...

in this paper, a useful classification of all lie subalgebras of a given lie algebraup to an inner automorphism is presented. this method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. after main results, we have applied this procedure for classifying the lie subalgebras of some examples of lie al...

The problem of non-solvable contractions of Lie algebras is analyzed. By means of a stability theorem, the problem is shown to be deeply related to the embeddings among semisimple Lie algebras and the resulting branching rules for representations. With this procedure, we determine all deformations of indecomposable Lie algebras having a nontrivial Levi decomposition onto semisimple Lie algebras...

This paper is devoted to the construction of Hom-Leibniz H-pseudoalgebras, which unify Hom-Lie Leibniz H-pseudoalgebras and algebras. Firstly, we give theorem obtain a class H-pseudoalgebras. We also construct Hom- from different perspectives, including (resp. Hom-Lie, Hom-associative) their representations, Homassociative) Thenwegive some properties representations Hom-LeibnizH-pseudoalgebras....

This paper acts as an introduction to representation theory. In addition to defining representations of Lie algebras and of finite groups, this paper will go through two standard examples, the Lie algebra sl2C and the finite group Sn, to illustrate techniques for their construction and use. In addition, those examples will develop some important theory behind representations of Lie algebras and...