The universal central extension of the holomorphic current algebra

2003 ◽  
Vol 112 (4) ◽  
pp. 441-458 ◽  
Author(s):  
Karl-Hermann Neeb ◽  
Friedrich Wagemann
Keyword(s):  
Current Algebra ◽  
Central Extension ◽  
Universal Central Extension

scholarly journals Universal central extensions of Lie–Rinehart algebras

2018 ◽  
Vol 17 (07) ◽  
pp. 1850134 ◽  
Author(s):  
J. L. Castiglioni ◽  
X. García-Martínez ◽  
M. Ladra
Keyword(s):  
Tensor Product ◽  
Lie Algebras ◽  
Central Extension ◽  
Universal Central Extension ◽  
Central Extensions ◽  
Definition Of ◽  
Universal Central Extensions

In this paper, we study the universal central extension of a Lie–Rinehart algebra and we give a description of it. Then we study the lifting of automorphisms and derivations to central extensions. We also give a definition of a non-abelian tensor product in Lie–Rinehart algebras based on the construction of Ellis of non-abelian tensor product of Lie algebras. We relate this non-abelian tensor product to the universal central extension.

The q-Analog Klein Bottle Lie Algebra

2014 ◽  
Vol 21 (04) ◽  
pp. 561-574
Author(s):  
Cuipo Jiang ◽  
Jingjing Jiang ◽  
Yufeng Pei
Keyword(s):  
Lie Algebra ◽  
Bilinear Form ◽  
Central Extension ◽  
Klein Bottle ◽  
Universal Central Extension ◽  
Finitely Generated ◽  
Invariant Bilinear Form ◽  
Infinite Dimensional ◽  
Simple Lie Algebra ◽  
Infinite Dimensional Lie Algebra

In this paper, we study an infinite-dimensional Lie algebra ℬq, called the q-analog Klein bottle Lie algebra. We show that ℬq is a finitely generated simple Lie algebra with a unique (up to scalars) symmetric invariant bilinear form. The derivation algebra and the universal central extension of ℬq are also determined.

Lie algebra extensions of current algebras on S3

2015 ◽  
Vol 12 (09) ◽  
pp. 1550087 ◽  
Author(s):  
Tosiaki Kori ◽  
Yuto Imai
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Lie Algebra ◽  
Current Algebra ◽  
Central Extension ◽  
Mathematical Tool ◽  
Two Dimensional ◽  
Root Space ◽  
Moody Algebra ◽  
Conformal Field

An affine Kac–Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac–Moody algebras give it for two-dimensional conformal field theory.

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