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.

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.

scholarly journals A combinatorial identity for the derivative of a theta series of a finite type root lattice

2003 ◽  
Vol 172 ◽  
pp. 1-30
Author(s):  
Satoshi Naito
Keyword(s):  
Representation Theory ◽  
Lie Algebra ◽  
Finite Type ◽  
Cartan Subalgebra ◽  
Theta Series ◽  
Combinatorial Identity ◽  
Root Lattice ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Affine Lie Algebra

AbstractLet be a (not necessarily simply laced) finite-dimensional complex simple Lie algebra with the Cartan subalgebra and Q ⊂ * the root lattice. Denote by ΘQ(q) the theta series of the root lattice Q of . We prove a curious “combinatorial” identity for the derivative of ΘQ(q), i.e. for by using the representation theory of an affine Lie algebra.

A New Class of Representations of EALA Coordinated by Quantum Tori in Two Variables

2002 ◽  
Vol 45 (4) ◽  
pp. 672-685 ◽  
Author(s):  
S. Eswara Rao ◽  
Punita Batra
Keyword(s):  
Lie Algebras ◽  
Primitive Root ◽  
Irreducible Module ◽  
Affine Lie Algebras ◽  
Quantum Torus ◽  
New Class ◽  
Root Of Unity ◽  
Quantum Tori ◽  
Finite Dimensional

AbstractWe study the representations of extended affine Lie algebras where q is N-th primitive root of unity (ℂq is the quantum torus in two variables). We first prove that ⊕ for a suitable number of copies is a quotient of . Thus any finite dimensional irreducible module for ⊕ lifts to a representation of . Conversely, we prove that any finite dimensional irreducible module for comes from above. We then construct modules for the extended affine Lie algebras which is integrable and has finite dimensional weight spaces.

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)).

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