Central extensions of Lie algebras graded by finite root systems

2000 ◽  
Vol 316 (3) ◽  
pp. 499-527 ◽  
Author(s):  
Bruce Allison ◽  
Georgia Benkart ◽  
Yun Gao
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Central Extensions

scholarly journals Integrating central extensions of Lie algebras via Lie 2-groups

2016 ◽  
Vol 18 (6) ◽  
pp. 1273-1320 ◽  
Author(s):  
Christoph Wockel ◽  
Chenchang Zhu
Keyword(s):  
Lie Algebras ◽  
Central Extensions

scholarly journals Lorentzian Toda field theories

2021 ◽  
pp. 2150017
Author(s):  
Andreas Fring ◽  
Samuel Whittington
Keyword(s):  
Lie Algebras ◽  
Mass Spectra ◽  
Energy Momentum Tensor ◽  
Root Systems ◽  
Momentum Tensor ◽  
Field Theories ◽  
Simple Lie Algebras ◽  
Different Types ◽  
Algebraic Framework ◽  
Complex Valued

We propose several different types of construction principles for new classes of Toda field theories based on root systems defined on Lorentzian lattices. In analogy to conformal and affine Toda theories based on root systems of semi-simple Lie algebras, also their Lorentzian extensions come about in conformal and massive variants. We carry out the Painlevé integrability test for the proposed theories, finding in general only one integer valued resonance corresponding to the energy-momentum tensor. Thus most of the Lorentzian Toda field theories are not integrable, as the remaining resonances, that grade the spins of the W-algebras in the semi-simple cases, are either non-integer or complex valued. We analyze in detail the classical mass spectra of several massive variants. Lorentzian Toda field theories may be viewed as perturbed versions of integrable theories equipped with an algebraic framework.

scholarly journals Central extensions of the quasi-orthogonal Lie algebras

1998 ◽  
Vol 31 (5) ◽  
pp. 1373-1394 ◽  
Author(s):  
J A de Azcárraga ◽  
F J Herranz ◽  
J C Pérez Bueno ◽  
M Santander
Keyword(s):  
Lie Algebras ◽  
Central Extensions

Central Extensions and Derivations of Generalized Schrödinger-Virasoro Algebras

2012 ◽  
Vol 19 (04) ◽  
pp. 735-744 ◽  
Author(s):  
Wei Wang ◽  
Junbo Li ◽  
Bin Xin
Keyword(s):  
Lie Algebras ◽  
Natural Generalization ◽  
Additive Subgroup ◽  
Central Extensions ◽  
Infinite Dimensional

Let 𝔽 be a field of characteristic 0, G an additive subgroup of 𝔽, s ∈ 𝔽 such that s ∉ G and 2s ∈ G. A class of infinite-dimensional Lie algebras [Formula: see text] called generalized Schrödinger-Virasoro algebras was defined by Tan and Zhang, which is a natural generalization of Schrödinger-Virasoro algebras. In this paper, central extensions and derivations of [Formula: see text] are determined.

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