Quantizations of the Extended Affine Lie Algebra $\widetilde{\frak{sl}_2(\mathbb{C}_q)}$

In this paper, the extended affine Lie algebra [Formula: see text] is quantized from three different points of view, which produces three non-commutative and non-cocommutative Hopf algebra structures, and yields other three quantizations by an isomorphism of [Formula: see text] correspondingly. Moreover, two of these quantizations can be restricted to the extended affine Lie algebra [Formula: see text].

Integrable Representations for the Extended Affine Lie Algebra Coordinated by Quantum Tori in Two Variables

In this paper we classify the irreducible integrable modules for the core of the extended affine Lie algebra of type Ad-1 coordinated by ℂq with finite-dimensional weight spaces and the center acting trivially, where ℂq is the quantum torus in two variables.

The Kostrikin Radical and the Invariance of the Core of Reduced Extended Affine Lie Algebras

In this paper we prove that the Kostrikin radical of an extended affine Lie algebra of reduced type coincides with the center of its core, and use this characterization to get a type-free description of the core of such algebras. As a consequence we get that the core of an extended affine Lie algebra of reduced type is invariant under the automorphisms of the algebra.

Fermionic and Bosonic Representations of the Extended Affine Lie Algebra

We construct a class of fermions (or bosons) by using a Clifford (or Weyl) algebra to get two families of irreducible representations for the extended affine Lie algebra of level (1, 0) (or (−1, 0)).