Central extensions and invariant forms of cartan type Lie algebras of positive characteristic

1985 ◽  
Vol 18 (4) ◽  
pp. 331-332 ◽  
Author(s):  
A. S. Dzhumadil'daev
Keyword(s):  
Lie Algebras ◽  
Positive Characteristic ◽  
Central Extensions ◽  
Cartan Type

Dual Space Derivations and H2(L, F) of Modular Lie Algebras

1987 ◽  
Vol 39 (5) ◽  
pp. 1078-1106 ◽  
Author(s):  
Rolf Farnsteiner
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Cohomology Group ◽  
Dual Space ◽  
Positive Characteristic ◽  
Base Field ◽  
Central Extensions ◽  
Simple Lie Algebras ◽  
Early Results ◽  
Modular Lie Algebras

It is well-known that the classical vanishing results of the cohomology theory of Lie algebras depend on the characteristic of the underlying base field. The theorems of Cartan and Zassenhaus, for instance, entail that non-modular simple Lie algebras do not admit non-trivial central extensions. In contrast, early results by Block [3] prove that this conclusion loses its validity if the underlying base field has positive characteristic.Central extensions of a given Lie algebra L, or equivalently its second cohomology group H(L, F), can be conveniently described by means of derivations φ:L → L*.

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

Restricted Envelopes of Lie Superalgebras

2015 ◽  
Vol 22 (02) ◽  
pp. 309-320
Author(s):  
Liping Sun ◽  
Wende Liu ◽  
Xiaocheng Gao ◽  
Boying Wu
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Cartan Type ◽  
Modular Lie Algebras ◽  
Modular Lie Superalgebras

Certain important results concerning p-envelopes of modular Lie algebras are generalized to the super-case. In particular, any p-envelope of the Lie algebra of a Lie superalgebra can be naturally extended to a restricted envelope of the Lie superalgebra. As an application, a theorem on the representations of Lie superalgebras is given, which is a super-version of Iwasawa's theorem in Lie algebra case. As an example, the minimal restricted envelopes are computed for three series of modular Lie superalgebras of Cartan type.

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