We present a systematic derivation for a general formula for the n-point coupling constant valid for affine Toda theories related to any simple Lie algebra g. All n-point couplings with n ≥ 4 are completely determined in terms of the masses and the three-point couplings. A general fusing rule, formulated in the root space of the Lie algebra, is derived for all n-point couplings.

‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...

In the representation theory, the classification and the construction of the irreducible representations are essential themes. In the first half of the twentieth century, I. Schur[11] introduced a prominent method to obtain the finite dimensional irreducible representations of the general linear group GL(n,C), or equivalently of its Lie algebra gl(n,C), which we call Schur-Weyl reciprocity at p...

Braided Lie algebras and bicovariant differential calculi over co-quasitriangular Hopf algebras. Abstract We show that if g Γ is the quantum tangent space (or quantum Lie algebra in the sense of Woronowicz) of a bicovariant first order differential calculus over a co-quasitriangular Hopf algebra (A, r), then a certain extension of it is a braided Lie algebra in the category of A-comodules. This...

We construct new families of examples of (real) Anosov Lie algebras starting with algebraic units. We also give examples of indecomposable Anosov Lie algebras (not a direct sum of proper Lie ideals) of dimension 13 and 16, and we conclude that for every n ≥ 6 with n 6= 7 there exists an indecomposable Anosov Lie algebra of dimension n.

Given a Lie algebra g over a field of characteristic zero k, let μ(g) = min{dimπ : π is a faithful representation of g}. Let hm be the Heisenberg Lie algebra of dimension 2m + 1 over k and let k[t] be the polynomial algebra in one variable. Given m ∈ N and p ∈ k[t], let hm,p = hm ⊗ k[t]/(p) be the current Lie algebra associated to hm and k[t]/(p), where (p) is the principal ideal in k[t] genera...

A Leibniz n-algebra is a vector space equipped with an n-ary operation which has the property of being a derivation for itself. This property is crucial in Nambu mechanics. For n ˆ 2 this is the notion of Leibniz algebra. In this paper we prove that the free Leibniz …n‡ 1†algebra can be described in terms of the n-magma, that is the set of n-ary planar trees. Then it is shown that the n-tensor ...

We have discovered that the gauge invariant observables of matrix models invariant under U(N) form a Lie algebra, in the planar large-N limit. These models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We study here the gauge invariant states corresponding to open strings ('mesons'). We find that the algebra is an extension of a remarkable new Lie algebra V Λ by a product o...