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Algebra di Lie semisemplice.
In matematica, un'algebra di Lie si dice semisemplice se è somma diretta di algebre di Lie semplici, ovvero di algebre di Lie non abeliane e i cui unici ideali sono 0 e stesso.
Equivalentemente, un'algebra di Lie è semisemplice se e solo se:
- La sua forma di Killing è non degenere.
- non ha ideali abeliani diversi da 0.
- non ha ideali risolubili diversi da 0.
- Il radicale di è 0.
- Humphreys, James E. Introduction to Lie Algebras and Representation Theory. Graduate Texts in Mathematics, 9. Springer-Verlag, New York, 1972. ISBN 0-387-90053-5
- Nicolas Bourbaki, VIII: Split Semi-simple Lie Algebras, in Elements of Mathematics: Lie Groups and Lie Algebras: Chapters 7–9, 2005.
- Karin Erdmann e Mark Wildon, Introduction to Lie Algebras, 1st, Springer, 2006, ISBN 1-84628-040-0.
- James E. Humphreys, Introduction to Lie Algebras and Representation Theory, Berlin, New York, Springer-Verlag, 1972, ISBN 978-0-387-90053-7.
- V. S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations, 1st, Springer, 2004, ISBN 0-387-90969-9.
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Algebra di Lie semisemplice
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