scholarly journals Central Extension of Quadratic Lie Algebras and Its Relation to Dihedral Homology

1996 ◽  
Vol 180 (3) ◽  
pp. 725-756
Author(s):  
Guillermo Cortiñas ◽  
Jack M. Shapiro
Keyword(s):  
Lie Algebras ◽  
Central Extension ◽  
Dihedral Homology

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 Twisted Vertex Operators and Unitary Lie Algebras

2015 ◽  
Vol 67 (3) ◽  
pp. 573-596 ◽  
Author(s):  
Fulin Chen ◽  
Yun Gao ◽  
Naihuan Jing ◽  
Shaobin Tan
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Polynomial Ring ◽  
Central Extension ◽  
Laurent Polynomial ◽  
New Method ◽  
Vertex Operators ◽  
Irreducible Decomposition ◽  
Laurent Polynomial Ring

AbstractA representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral ℤ2–lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by–product, some fundamental representations of affine Kac–Moody Lie algebra of type A(2)n are recovered by the new method.

q-Deformations of 3-Lie Algebras

2017 ◽  
Vol 24 (03) ◽  
pp. 519-540 ◽  
Author(s):  
Ruipu Bai ◽  
Lixin Lin ◽  
Yan Zhang ◽  
Chuangchuang Kang
Keyword(s):  
Vector Space ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Central Extension ◽  
Jacobi Identity ◽  
Group Algebras ◽  
Type I ◽  
Associative Algebras

q-Deformations of 3-Lie algebras and representations of q-3-Lie algebras are discussed. A q-3-Lie algebra [Formula: see text], where [Formula: see text] and [Formula: see text], is a vector space A over a field 𝔽 with 3-ary linear multiplications [ , , ]q and [Formula: see text] from [Formula: see text] to A, and a map [Formula: see text] satisfying the q-Jacobi identity [Formula: see text] for all [Formula: see text]. If the multiplications satisfy that [Formula: see text] and [Formula: see text] is skew-symmetry, then [Formula: see text] is called a type (I)-q-3- Lie algebra. From q-Lie algebras, group algebras and commutative associative algebras, q-3-Lie algebras and type (I)-q-3-Lie algebras are constructed. Also, the non-trivial onedimensional central extension of q-3-Lie algebras is investigated, and new q-3-Lie algebras [Formula: see text], and [Formula: see text] are obtained.

SOME PROPERTIES ON THE SCHUR MULTIPLIER OF A PAIR OF LIE ALGEBRAS

2012 ◽  
Vol 11 (01) ◽  
pp. 1250011 ◽  
Author(s):  
MOHAMMAD REZA RISMANCHIAN ◽  
MEHDI ARASKHAN
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Central Extension ◽  
Sufficient Condition ◽  
Schur Multiplier ◽  
Necessary And Sufficient Condition ◽  
Pair Of Lie Algebras ◽  
Necessary And Sufficient

The aim of this paper is to introduce the concept of the Schur multiplier [Formula: see text] of a pair of Lie algebras and to obtain some inequalities for the dimension of [Formula: see text]. Also, we consider some of the features of central extension of an arbitrary Lie algebra. Moreover, we present a necessary and sufficient condition in which the Schur multiplier of a pair of Lie algebras can be embedded into the Schur multiplier of their factor Lie algebras.

On isomorphism criterion for a subclass of complex filiform Leibniz algebras

2017 ◽  
Vol 27 (07) ◽  
pp. 953-972
Author(s):  
I. S. Rakhimov ◽  
A. Kh. Khudoyberdiyev ◽  
B. A. Omirov ◽  
K. A. Mohd Atan
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Central Extension ◽  
Linear Deformation ◽  
Leibniz Algebras ◽  
Structure Constants ◽  
Filiform Lie Algebras ◽  
Filiform Lie Algebra ◽  
Isomorphism Criterion

In this paper, we present an algorithm to give the isomorphism criterion for a subclass of complex filiform Leibniz algebras arising from naturally graded filiform Lie algebras. This subclass appeared as a Leibniz central extension of a linear deformation of filiform Lie algebra. We give the table of multiplication choosing appropriate adapted basis, identify the elementary base changes and describe the behavior of structure constants under these base changes, then combining them the isomorphism criterion is given. The final result of calculations for one particular case also is provided.

scholarly journals MODULES FOR A SHEAF OF LIE ALGEBRAS ON LOOP MANIFOLDS

2012 ◽  
Vol 23 (08) ◽  
pp. 1250079
Author(s):  
YULY BILLIG
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Semidirect Product ◽  
Central Extension ◽  
Vector Fields ◽  
Vertex Algebra ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Rham Complex ◽  
De Rham

We consider a semidirect product of the sheaf of vector fields on a manifold ℂ* × X with a central extension of the sheaf of Lie algebras of maps from ℂ* × X into a finite-dimensional simple Lie algebra, viewed as sheaves on X. Using vertex algebra methods we construct sheaves of modules for this sheaf of Lie algebras. Our results extend the work of Malikov–Schechtman–Vaintrob on the chiral de Rham complex.

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