Differential operators in the classification of simple modular Lie algebras

1992 ◽  
Vol 47 (4) ◽  
pp. 212-213
Author(s):  
M I Kuznetsov
Keyword(s):  
Lie Algebras ◽  
Differential Operators ◽  
Modular Lie Algebras

scholarly journals Contributions to the classification of simple modular Lie algebras

1994 ◽  
Vol 341 (1) ◽  
pp. 227-252 ◽  
Author(s):  
Georgia Benkart ◽  
J. Marshall Osborn ◽  
Helmut Strade
Keyword(s):  
Lie Algebras ◽  
Modular Lie Algebras

scholarly journals Formal Pseudodifferential Operators in One and Several Variables, Central Extensions, and Integrable Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Jarnishs Beltran ◽  
Enrique G. Reyes
Keyword(s):  
Lie Algebras ◽  
Nonlinear Equations ◽  
Integrable Systems ◽  
Differential Operators ◽  
Pseudodifferential Operators ◽  
Central Extensions ◽  
Several Variables ◽  
Zero Curvature ◽  
Manin Triples

We review some aspects of the theory of Lie algebras of (twisted and untwisted) formal pseudodifferential operators in one and several variables in a general algebraic context. We focus mainly on the construction and classification of nontrivial central extensions. As applications, we construct hierarchies of centrally extended Lie algebras of formal differential operators in one and several variables, Manin triples and hierarchies of nonlinear equations in Lax and zero curvature form.

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