Semisimple Lie Algebras

Xiaoping Xu ()
Additional contact information
Xiaoping Xu: Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Institute of Mathematics

Chapter Chapter 2 in Representations of Lie Algebras and Partial Differential Equations, 2017, pp 33-59 from Springer

Abstract: Abstract We use the Killing form to derive the decomposition of a finite-dimensional semisimple Lie algebra over $$\mathbb {C}$$ C into a direct sum of simple ideals. Moreover, we prove the Weyl’s theorem of complete reducibility, and the equivalence of the complete reducibility of real and complex modules is also given. Cartan’s root-space decomposition of a finite-dimensional semisimple Lie algebra over $$\mathbb {C}$$ C is derived.

Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-6391-6_2

Ordering information: This item can be ordered from
http://www.springer.com/9789811063916

DOI: 10.1007/978-981-10-6391-6_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().