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...

In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

William M. Singer’s theory of extensions of connected Hopf algebras is used to give a complete list of the cocommutative connected Hopf algebras over a field of positive characteristic p which have vector space dimension less than or equal to p3. The theory shows that there are exactly two noncommutative non-primitively generated Hopf algebras on the list, one of which is the Hopf algebra corre...

In this paper, using generating functions we study two categories E and C of modules for twisted affine Lie algebras ĝ[σ], which were firstly introduced and studied in [Li] for untwisted affine Lie algebras. We classify integrable irreducible ĝ[σ]-modules in categories E and C, where E is proved to contain the well known evaluation modules and C to unify highest weight modules, evaluation modul...

Vertex algebras provide an axiomatic algebraic description of the operator product expansion (OPE) of chiral fields in 2-dimensional conformal field theory. Vertex Lie algebras (= Lie conformal algebras) encode the singular part of the OPE, or, equivalently, the commutators of chiral fields. We discuss generalizations of vertex algebras and vertex Lie algebras, which are relevant for higher-dim...

In this work we consider the moduli space of all noncommutative metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over $\mathbb C$ and R$ up to dimension 5 algebras in 6. We introduce cyclic reduced cohomology identify their deformations.

Fomin and Zelevinsky [6] show that a certain two-parameter family of rational recurrence relations, here called the (b, c) family, possesses the Laurentness property: for all b, c, each term of the (b, c) sequence can be expressed as a Laurent polynomial in the two initial terms. In the case where the positive integers b, c satisfy bc < 4, the recurrence is related to the root systems of finite...

In this paper, we study a class of infinite simple Lie conformal algebras associated to generalized Block type algebras. The central extensions by one-dimensional center $\mathbb {C}\mathfrak {c}$ , derivations and free intermediate series modules are determined. Moreover, also show that these do not have any non-trivial finite modules. Consequently, cannot be embedded into gcN for positive int...

Fomin and Zelevinsky [9] show that a certain two-parameter family of rational recurrence relations, here called the (b, c) family, possesses the Laurentness property: for all b, c, each term of the (b, c) sequence can be expressed as a Laurent polynomial in the two initial terms. In the case where the positive integers b, c satisfy bc < 4, the recurrence is related to the root systems of finite...