Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy

1992 ◽  
Vol 108 (1) ◽  
pp. 323-347 ◽  
Author(s):  
S. Berman ◽  
R. V. Moody
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Matrix Algebras ◽  
Intersection Matrix

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.

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 On quantum Lie algebras and quantum root systems

1996 ◽  
Vol 29 (8) ◽  
pp. 1703-1722 ◽  
Author(s):  
Gustav W Delius ◽  
Andreas Hüffmann
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Quantum Lie Algebras

ROOT SYSTEMS ARISING FROM AUTOMORPHISMS

2012 ◽  
Vol 11 (03) ◽  
pp. 1250057 ◽  
Author(s):  
SAEID AZAM ◽  
MALIHE YOUSOSFZADEH
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Affine Lie Algebras ◽  
Combinatorial Approach ◽  
Reflection Algebras ◽  
Affine Root Systems ◽  
Outstanding Work ◽  
Affine Reflection

We study a combinatorial approach of producing new root systems from the old ones in the context of affine root systems and their new generalizations. The appearance of this approach in the literature goes back to the outstanding work of Kac in the realization of affine Kac–Moody Lie algebras. In recent years, this approach has been appeared in many other works, including the study of affinization of extended affine Lie algebras and invariant affine reflection algebras.

Lie algebras graded by the root systems 𝐵𝐶ᵣ,𝑟≥2

2002 ◽  
Vol 158 (751) ◽  
pp. 0-0 ◽  
Author(s):  
Bruce Allison ◽  
Georgia Benkart ◽  
Yun Gao
Keyword(s):  
Lie Algebras ◽  
Root Systems

Derivations and Invariant Forms of Lie Algebras Graded by Finite Root Systems

1998 ◽  
Vol 50 (2) ◽  
pp. 225-241 ◽  
Author(s):  
Georgia Benkart
Keyword(s):  
Lie Algebras ◽  
Adjoint Action ◽  
Root Systems ◽  
Bilinear Forms ◽  
Finite Dimensional ◽  
Completely Reducible

AbstractLie algebras graded by finite reduced root systems have been classified up to isomorphism. In this paper we describe the derivation algebras of these Lie algebras and determine when they possess invariant bilinear forms. The results which we develop to do this are much more general and apply to Lie algebras that are completely reducible with respect to the adjoint action of a finite-dimensional subalgebra.

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