Twisted toroidal Lie algebras and Moody-Rao-Yokonuma presentation

@article{Chen2019TwistedTL,
  title={Twisted toroidal Lie algebras and Moody-Rao-Yokonuma presentation},
  author={Fulin Chen and Naihuan Jing and Fei Kong and Shaobin Tan},
  journal={Science China Mathematics},
  year={2019},
  pages={1-20}
}
Let g be a (twisted or untwisted) affine Kac-Moody algebra, and μ be a diagram automorphism of g. In this paper, we give an explicit realization for the universal central extension ĝ[ μ ] of the twisted loop algebra of g with respect to μ , which provides a Moody-Rao-Yokonuma presentation for the algebra ĝ[ μ ] when μ , is non-transitive, and the presentation is indeed related to the quantization of twisted toroidal Lie algebras. 
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References

SHOWING 1-10 OF 44 REFERENCES
Quantum Kac-Moody Algebras and Vertex Representations
We introduce an affinization of the quantum Kac-Moody algebra associated to a symmet- ric generalized Cartan matrix. Based on the affinization, we construct a representation of the quantum Kac-MoodyExpand
Torsors, Reductive Group Schemes and Extended Affine Lie Algebras
We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play aExpand
Classification and construction of quasisimple Lie algebras
Abstract We study a class of (possibly infinite-dimensional) Lie algebras, called the Quasisimple Lie algebras (QSLA's), and generalizing semisimple and affine Kac-Moody Lie algebras. They areExpand
Quantum Tori and the Structure of Elliptic Quasi-simple Lie Algebras
Abstract We study and classify those tame irreducible elliptic quasi-simple Lie algebras which are simply laced and of rankl⩾3. The first step is to identify the core of such an algebra up to centralExpand
Toroidal Lie algebras and vertex representations
The paper describes the theory of the toroidal Lie algebra, i.e. the Lie algebra of polynomial maps of a complex torus ℂ××ℂ× into a finite-dimensional simple Lie algebra g. We describe the universalExpand
From Dynkin diagram symmetries to fixed point structures
Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebra g induces an automorphism of g and a mappingτω between highest weight modules of g. For a large class of such DynkinExpand
Multiloop realization of extended affine Lie algebras and Lie tori
An important theorem in the theory of infinite dimensional Lie algebras states that any affine Kac-Moody algebra can be realized (that is to say constructed explicitly) using loop algebras. In thisExpand
Vertex operator representations for toroidal Lie algebra of type B-l
Vertex operator representations for toroidal Lie algebras of simply-laced type were studied in [MRY] and [EM]. In this paper we give vertex operator constructions for the toroidal Lie algebra of typeExpand
Double-loop algebras and the Fock space
The fermionic Fock space admits two different actions of the quantized enveloping algebra of $\hat\sln$> The first one is a q-deformation of the well-known level-one representation of the affine LieExpand
Quantum Vertex Representations via Finite Groups¶and the McKay Correspondence
Abstract:We establish a q-analog of our recent work on vertex representations and the McKay correspondence. For each finite group Γ we construct a Fock space and associated vertex operators in termsExpand
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