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Introduction to Strings and Branes by Peter West

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16 String theory and Lie algebras

 

 

 

 

Everybody attributes the theory of Lie algebras to Cartan, but most of it was discovered by Killing, except that is the Killing form, which was found by Cartan.

This statement reflects the neglect of Killing’s work that occurred despite the clear credit given to it by Cartan

Lie algebras have played a crucial role in the formulation of the electromagnetic, nuclear weak and strong forces as well as many other areas of theoretical physics. As string theory aims to provide a single theory of physics it is not unlikely that Lie algebras will play a central role. With this in mind we first give, in this chapter, a review of finite-dimensional semi-simple Lie algebras, that is, those in the list of Cartan. ...

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