Isomorphisms, Conjugacy and Exceptional Types

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

Chapter Chapter 4 in Representations of Lie Algebras and Partial Differential Equations, 2017, pp 95-123 from Springer

Abstract: Abstract We show that the structure of a finite-dimensional semisimple Lie algebra over $$\mathbb {C}$$ C is completely determined by its root system. Moreover, we prove that any two Cartan subalgebras of such a Lie algebra $${\mathscr {G}}$$ G are conjugated under the group of inner automorphisms of $${\mathscr {G}}$$ G . In particular, the automorphism group of $${\mathscr {G}}$$ G is determined when it is simple. Furthermore, we give explicit constructions of the simple Lie algebras of exceptional types.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-6391-6_4

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DOI: 10.1007/978-981-10-6391-6_4

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