Central Extensions of Lie Algebras and Bargmann’s Theorem

2008 ◽  
pp. 63-73
Author(s):  
M. Schottenloher
Keyword(s):  
Lie Algebras ◽  
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 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 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

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.

Central extensions of 4-dimensional binary Lie algebras

2020 ◽  
Vol 50 (5) ◽  
pp. 1541-1559
Author(s):  
Hani Abdelwahab ◽  
Antonio J. Calderón Martín ◽  
Amir Fernández Ouaridi
Keyword(s):  
Lie Algebras ◽  
Central Extensions

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.

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