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The exponential image of simple complex lie groups of exceptional type

✍ Scribed by Dragomir Ž. Ðoković

Book ID
104653413
Publisher
Springer
Year
1988
Tongue
English
Weight
359 KB
Volume
27
Category
Article
ISSN
0046-5755

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✦ Synopsis

DOKOVIt~ THE EXPONENTIAL IMAGE OF SIMPLE COMPLEX LIE GROUPS OF EXCEPTIONAL TYPE

AaSTRACT. Let G be a connected reductive complex Lie group. Let E~ be the image of the exponential map of G and E' 6 its complement in G. We give a purely algebraic characterization of the set E 6 and also describe an algorithm for finding all conjugacy classes of G in E~. We are mainly interested in the case when the Lie algebra of G is simple and exceptional. Full details are provided for groups G of type G2, F4, and E 6. If G is of type G 2 then there are only two such conjugacy classes.

📜 SIMILAR VOLUMES

Matrix Generators for Exceptional Groups
Matrix Generators for Exceptional Groups of Lie Type
✍ R.B Howlett; L.J Rylands; D.E Taylor 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 337 KB

This paper gives a uniform method of constructing generators for matrix representations of finite groups of Lie type with particular emphasis on the exceptional groups. The algorithm constructs matrices for the action of root elements on the lowest dimension representation of an associated Lie algeb