scholarly journals Universal central extensions of Chevalley algebras over Laurent polynomial rings and GIM Lie algebras

1985 ◽  
Vol 61 (6) ◽  
pp. 179-181 ◽  
Author(s):  
Jun Morita ◽  
Yōji Yoshii
Keyword(s):  
Lie Algebras ◽  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Central Extensions ◽  
Universal 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.

scholarly journals n-Point Virasoro algebras and their modules of densities

2014 ◽  
Vol 16 (03) ◽  
pp. 1350047 ◽  
Author(s):  
Ben Cox ◽  
Xiangqian Guo ◽  
Rencai Lu ◽  
Kaiming Zhao
Keyword(s):  
Large Class ◽  
Lie Algebras ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Virasoro Algebra ◽  
Necessary And Sufficient Conditions ◽  
Genus Zero ◽  
Central Extensions ◽  
Necessary And Sufficient ◽  
Universal Central Extensions

In this paper we introduce and study n-point Virasoro algebras, [Formula: see text], which are natural generalizations of the classical Virasoro algebra and have as quotients multipoint genus zero Krichever–Novikov type algebras. We determine necessary and sufficient conditions for the latter two such Lie algebras to be isomorphic. Moreover we determine their automorphisms, their derivation algebras, their universal central extensions, and some other properties. The list of automorphism groups that occur is Cn, Dn, A4, S4 and A5. We also construct a large class of modules which we call modules of densities, and determine necessary and sufficient conditions for them to be irreducible.

scholarly journals Simple superelliptic Lie algebras

2017 ◽  
Vol 19 (03) ◽  
pp. 1650032 ◽  
Author(s):  
Ben Cox ◽  
Xiangqian Guo ◽  
Rencai Lu ◽  
Kaiming Zhao
Keyword(s):  
Lie Algebras ◽  
Riemann Surfaces ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Central Extensions ◽  
Birational Equivalence ◽  
Necessary And Sufficient ◽  
Universal Central Extensions

Let [Formula: see text], [Formula: see text]. Then we have the algebraic curve [Formula: see text], and its coordinate algebras (the Riemann surfaces) [Formula: see text] and [Formula: see text] The Lie algebras [Formula: see text] and [Formula: see text] are called the [Formula: see text]th superelliptic Lie algebras associated to [Formula: see text]. In this paper, we determine the necessary and sufficient conditions for such Lie algebras to be simple, and determine their universal central extensions and their derivation algebras. We also study the isomorphism and automorphism problem for these Lie algebras, which will help to understand the birational equivalence of some algebraic curves of the form [Formula: see text].

scholarly journals Universal central extensions of gauge algebras and groups

2012 ◽  
Vol 2013 (682) ◽  
pp. 129-139
Author(s):  
Bas Janssens ◽  
Christoph Wockel
Keyword(s):  
Lie Algebras ◽  
Lie Group ◽  
Central Extension ◽  
Compact Manifold ◽  
General Setting ◽  
Central Extensions ◽  
Universal Central Extensions

Abstract. We show that the canonical central extension of the group of sections of a Lie group bundle over a compact manifold, constructed by Neeb and Wockel (2009), is universal. In doing so, we prove universality of the corresponding central extension of Lie algebras in a slightly more general setting.

Generalized Affine Kac-Moody Lie Algebras Over Localizations of the Polynomial Ring in One Variable

1994 ◽  
Vol 37 (1) ◽  
pp. 21-28 ◽  
Author(s):  
Murray Bremner
Keyword(s):  
Commutative Ring ◽  
Lie Algebras ◽  
Polynomial Ring ◽  
Simple Complex ◽  
Central Extensions ◽  
Commutation Relations ◽  
Universal Central Extensions

AbstractWe consider simple complex Lie algebras extended over the commutative ring C[z,(z — a1)-1, . . . ,(z — an)-1] where a1, . . . ,an ∊ C. We compute the universal central extensions of these Lie algebras and present explicit commutation relations for these extensions. These algebras generalize the untwisted affine Kac-Moody Lie algebras, which correspond to the case n = 1, a1 = 0.

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