Representation theory of semisimple Lie algebras

1987 ◽  
pp. 21-28
Author(s):  
Thomas Enright
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Semisimple Lie Algebras

scholarly journals Airy Structures for Semisimple Lie Algebras

2021 ◽  
Author(s):  
Leszek Hadasz ◽  
Błażej Ruba
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Complete Classification ◽  
Semiclassical Analysis ◽  
Simple Lie Algebras ◽  
Semisimple Lie Algebras ◽  
Gauge Transformations ◽  
Finite Dimensional ◽  
Countably Infinite

AbstractWe give a complete classification of Airy structures for finite-dimensional simple Lie algebras over $${\mathbb {C}}$$ C , and to some extent also over $${\mathbb {R}}$$ R , up to isomorphisms and gauge transformations. The result is that the only algebras of this type which admit any Airy structures are $$\mathfrak {sl}_2$$ sl 2 , $$\mathfrak {sp}_4$$ sp 4 and $$\mathfrak {sp}_{10}$$ sp 10 . Among these, each admits exactly two non-equivalent Airy structures. Our methods apply directly also to semisimple Lie algebras. In this case it turns out that the number of non-equivalent Airy structures is countably infinite. We have derived a number of interesting properties of these Airy structures and constructed many examples. Techniques used to derive our results may be described, broadly speaking, as an application of representation theory in semiclassical analysis.

Semisimple Lie Algebras of Operators

2001 ◽  
pp. 181-202
Author(s):  
Daniel Beltiţă ◽  
Mihai Şabac
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras
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