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The author begins with a summary of these general theorems and then discusses in detail the structure and representation theory of complex semisimple Lie algebras.
This paper introduces Lie groups and their associated Lie algebras. With the goal of describing simple Lie groups, we analyze semisimple complex Lie algebras by their root systems to classify simple Lie algebras. We assume a background in linear algebra, di erential manifolds, and covering spaces.
In this chapter, we begin the study of semisimple Lie algebras and their representations. This is one of the highest achievements of the theory of Lie algebras, which has numerous applications (for example, to physics), not to mention that it is also one of the most beautiful areas of mathematics.
A connected Lie group is called semisimple if its Lie algebra is a semisimple Lie algebra, i.e. a direct sum of simple Lie algebras. It is called reductive if its Lie algebra is a direct sum of simple and trivial (one-dimensional) Lie algebras.
The theme of this chapter is an investigation of complex semisimple Lie algebras by a two-step process, first by passing from such a Lie algebra to a reduced abstract root system via a choice of Cartan subalgebra and then by passing from the root system to an...
2 de jun. de 2022 · Translation of: Algèbres de Lie semi-simples complexes Bibliography: p. 71-72 Includes index
En matemáticas, un álgebra de Lie semi-simple si es un álgebra de Lie que es suma directa de álgebras de Lie simples (álgebras de Lie no abelianas sin ningún ideal propio no nulo). A lo largo del artículo, a menos que se indique lo contrario, un álgebra de Lie es un álgebra de Lie de dimensión finita sobre un campo de ...
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