Fermionic and Bosonic Representations of the Extended Affine Lie Algebra

2002 ◽  
Vol 45 (4) ◽  
pp. 623-633 ◽  
Author(s):  
Yun Gao
Keyword(s):  
Lie Algebra ◽  
Weyl Algebra ◽  
Irreducible Representations ◽  
Affine Lie Algebra ◽  
Level 1 ◽  
Extended Affine Lie Algebra

AbstractWe 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)).

scholarly journals FUSION RULES AND COMPLETE REDUCIBILITY OF CERTAIN MODULES FOR AFFINE LIE ALGEBRAS

2013 ◽  
Vol 13 (01) ◽  
pp. 1350062 ◽  
Author(s):  
DRAŽEN ADAMOVIĆ ◽  
OZREN PERŠE
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Operator Algebras ◽  
Affine Lie Algebras ◽  
Fusion Rules ◽  
Type Formula ◽  
Complete Reducibility ◽  
Affine Lie Algebra ◽  
Branching Rules ◽  
Level 1

We develop a new method for obtaining branching rules for affine Kac–Moody Lie algebras at negative integer levels. This method uses fusion rules for vertex operator algebras of affine type. We prove that an infinite family of ordinary modules for affine vertex algebra of type A investigated in our previous paper J. Algebra319 (2008) 2434–2450, is closed under fusion. Then, we apply these fusion rules on explicit bosonic realization of level -1 modules for the affine Lie algebra of type [Formula: see text], obtain a new proof of complete reducibility for these representations, and the corresponding decomposition for ℓ ≥ 3. We also obtain the complete reducibility of the associated level -1 modules for affine Lie algebra of type [Formula: see text]. Next, we notice that the category of [Formula: see text] modules at level -2ℓ + 3 has the isomorphic fusion algebra. This enables us to decompose certain [Formula: see text] and [Formula: see text]-modules at negative levels.

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

2008 ◽  
Vol 51 (2) ◽  
pp. 298-309 ◽  
Author(s):  
Maribel Tocón
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Affine Lie Algebras ◽  
The Core ◽  
Affine Lie Algebra ◽  
Extended Affine Lie Algebra

AbstractIn 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.

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

2014 ◽  
Vol 21 (03) ◽  
pp. 535-540 ◽  
Author(s):  
Fei Kong ◽  
Zhiqiang Li ◽  
Shaobin Tan ◽  
Qing Wang
Keyword(s):  
Lie Algebra ◽  
Type A ◽  
Quantum Torus ◽  
The Core ◽  
Quantum Tori ◽  
Finite Dimensional ◽  
Affine Lie Algebra ◽  
Extended Affine Lie Algebra ◽  
Integrable Modules

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.

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

2015 ◽  
Vol 22 (04) ◽  
pp. 581-602 ◽  
Author(s):  
Ying Xu ◽  
Junbo Li
Keyword(s):  
Hopf Algebra ◽  
Lie Algebra ◽  
Affine Lie Algebra ◽  
Points Of View ◽  
Extended Affine Lie Algebra ◽  
Cocommutative Hopf Algebra

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].

Sign in / Sign up

Export Citation Format

Share Document