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MR 42 Zbl Topologie des groupes de Lie, Paris, Springer , Some arithmetical results on semi-simple Lie algebras Publ. Springer and R. Steinberg , Conjugacy classes.

Lectures on Lie Groups and Lie Algebras (London Mathematical Society Student Texts, #32)

Steinberg , Prime power representations of finite linear groups, II Can. MR 19,d Zbl Steinberg , Representations of algebraic groups Nagoya Math. MR 27 Zbl Steinberg , Regular elements of semisimple algebraic groups Publ. Numdam MR 31 Zbl Verma , Structure of certain induced representations of complex semisimple Lie algebras Dissertation, Yale University, Zassenhaus , The representations of Lie algebras of prime characteristic Proc.

Selecting your course units

Glasgow Math. MR 16,c Zbl Journals Seminars Books Theses Authors. Between and. The center of the universal enveloping algebra of a Lie algebra in characteristic p.

Veldkamp, F. References [1] A.

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In characteristic 0 studying the groups is almost equivalent to studying the Lie algebras and their representations. This line of research doesn't necessarily reveal much that is new about Lie groups, but it does place those groups in a framework which extends to other fields, etc.

Reine Angew. Still, for most practical purposes it's enough to follow the classical outline of E. Cartan and others, relating real groups or Lie algebras and their representations to the complexifications. For the results concerning highest weigts etc. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 5 years, 9 months ago. Active 5 years, 9 months ago.

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Viewed times. Comparison of real and complex forms of the Lie algebras, along with their finite dimensional representations, goes back a century or so. Most approaches to classification rely on working out the easier complex case first, then studying restriction to real forms and extension of scalars. See for example Helgason's books.

Lie Groups and Lie Algebras - Lecture 2

I explained it in the comment to the answer given by Dietrich. Jim Humphreys Jim Humphreys