# 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.
4 Citations
Extended affine Lie algebras, vertex algebras and equivariant $\phi$-coordinated quasi modules
For any nullity 2 extended affine Lie algebra E of maximal type and l ∈ C, we prove that there exist a vertex algebra VE(l) and an automorphism group G of VE(l) equipped with a linear character χ,
Drinfeld-type presentations of loop algebras
• Mathematics
• 2019
Let $\mathfrak{g}$ be the derived subalgebra of a Kac-Moody Lie algebra of finite type or affine type, $\mu$ a diagram automorphism of $\mathfrak{g}$ and $L(\mathfrak{g},\mu)$ the loop algebra of
Twisted quantum affinizations and quantization of extended affine Lie algebras
• Mathematics
• 2020
In this paper, for an arbitrary Kac-Moody Lie algebra $\mathfrak{g}$ and a diagram automorphism $\mu$ of $\mathfrak{g}$ satisfying two linking conditions, we introduce and study a $\mu$-twisted
Representations of twisted toroidal Lie algebras from twisted modules over vertex algebras
• Mathematics, Physics
Journal of Mathematical Physics
• 2020
Given a simple finite-dimensional Lie algebra and an automorphism of finite order, one defines the notion of a twisted toroidal Lie algebra. In this paper, we construct representations of twisted

## 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-Moody
Torsors, Reductive Group Schemes and Extended Affine Lie Algebras
• Mathematics
• 2011
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 a
Classification and construction of quasisimple Lie algebras
• Mathematics
• 1986
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 are
Quantum Tori and the Structure of Elliptic Quasi-simple Lie Algebras
• Mathematics
• 1996
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 central
Toroidal Lie algebras and vertex representations
• Mathematics
• 1990
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 universal
From Dynkin diagram symmetries to fixed point structures
• Physics, Mathematics
• 1995
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 Dynkin
Multiloop realization of extended affine Lie algebras and Lie tori
• Mathematics
• 2007
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 this
Vertex operator representations for toroidal Lie algebra of type B-l
• Mathematics
• 1999
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 type
Double-loop algebras and the Fock space
• Mathematics
• 1996
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 Lie
Quantum Vertex Representations via Finite Groups¶and the McKay Correspondence
• Physics, Mathematics
• 1999
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 terms