• ei, fi. e1 = 1⊗ E1, e2 = 1⊗ E2; f1 = 1⊗ F1, f2 = 1⊗ F2. • e0, f0, h0. e0 = t⊗ [F1, F2] = t⊗ E31. f0 = t −1 ⊗ [E1, E2] = t−1 ⊗ E13. h0 = [e0, f0] = −1⊗ (H1 +H2) + c = −1⊗ (E11 + E33) + c • H. H = 1⊗H ⊕ Cc⊕ Cd. Note that c is just the central element c = h0 + h1 + h2. • Π. α1 = 1 = 2, α1(c) = α1(d) = 0 α2 = 1 = 2, α1(c) = α1(d) = 0 θ = α1 + α2 = 1 − 3, θ(c) = θ(d) = 0 δ : δ(1⊗H) = δ(c) = 0, δ(d...

Abstract. In this paper, we provide a new formulation for the generalized periodic Toda lattice. Since the work of Kostant, Adler and Symes, it has been known that the Toda lattice is related to the structure of simple Lie algebras. Indeed, the non-periodic and the periodic Toda lattices can be expressed as Hamiltonian systems on coadjoint orbits: the former of a simple Lie group and the latter...

Braided-Lie bialgebras have been introduced by Majid, as the Lie versions of Hopf algebras in braided categories. In this paper we extend previous work of Majid and of ours to show that there is a braided-Lie bialgebra associated to each inclusion of Kac–Moody bialgebras. Doing so, we obtain many new examples of infinite-dimensional braided-Lie bialgebras. We analyze further the case of untwist...

We construct an irreducible representation for the extended affine algebra of type sl2 with coordinates in a quantum torus. We explicitly give formulas using vertex operators similar to those found in the theory of the infinite rank affine algebra A∞. Introduction. The purpose of this paper is to construct a module for the Extended Affine Lie algebra (EALA for short), we call it L̂, of type sl2 ...

We present a systematic construction of classical extended superconformal algebras from the hamiltonian reduction of a class of affine Lie superalgebras, which include an even subalgebra sl(2). In particular, we obtain the doubly extended N = 4 superconformal algebra Ãγ from the hamiltonian reduction of the exceptional Lie superalgebra D(2|1; γ/(1− γ)). We also find the Miura transformation for...

In ‎this ‎paper, ‎we ‎study ‎the ‎relation ‎between ‎the ‎soft ‎sets ‎and ‎soft ‎Lie ‎algebras ‎with ‎the ‎lattice theory. ‎We ‎introduce ‎the ‎concepts ‎of ‎the ‎lattice ‎of ‎soft ‎sets, ‎full ‎soft ‎sets ‎and ‎soft ‎Lie ‎algebras ‎and next, we ‎verify ‎some ‎properties ‎of ‎them. We ‎prove ‎that ‎the ‎lattice ‎of ‎the ‎soft ‎sets ‎on ‎a fixed parameter set is isomorphic to the power set of a ...

We prove complete reducibility for an integrable module for an affine Lie algebra where the canonical central element acts non-trivially. We further prove that integrable modules does not exists for most of the super affine Lie algebras where the center acts non-trivially. 1 2000 Mathematics subject classification primary 17B65, 17B68

In this paper, we discuss the pair problem of generators in affine Kac-Moody Lie algebras. For any affine Kac-Moody algebra g(A) of X l type and arbitrary nonzero imaginary root vector x, we prove that there exists some y ∈ g(A), such that g′(A) is contained in the Lie algebra generated by x and y.