On the universal central extension of superelliptic affine Lie algebras

2021 ◽  
pp. 1-11
Author(s):  
Felipe Albino dos Santos
Keyword(s):  
Lie Algebras ◽  
Central Extension ◽  
Affine Lie Algebras ◽  
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.

A class of non-standard modules for affine Lie algebras

1987 ◽  
Vol 196 (3) ◽  
pp. 303-313 ◽  
Author(s):  
Nolan R. Wallach
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras

QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

1992 ◽  
Vol 07 (20) ◽  
pp. 4885-4898 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Quantum Hamiltonian Reduction ◽  
Free Field Realization ◽  
Coset Construction ◽  
Quantum Hamiltonian

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

scholarly journals Braided Tensor Categories of Admissible Modules for Affine Lie Algebras

2018 ◽  
Vol 362 (3) ◽  
pp. 827-854 ◽  
Author(s):  
Thomas Creutzig ◽  
Yi-Zhi Huang ◽  
Jinwei Yang
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Tensor Categories
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