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Invariant lattices in Lie algebras and their automorphism groups. (English) Zbl 0678.17007
Group theory, Proc. Conf., Singapore 1987, 171-181 (1989).
[For the entire collection see Zbl 0652.00004.]
In this lecture, marking that the different natural realizations of various types of simple groups now become more significant the author describes some approach to the realization problem. The basic idea is that of obtaining an orthogonal decomposition of a certain complex simple Lie algebra L. Some results are mentioned. Some problems are suggested, for instance, the so called generalized problem of Winnie-the-Pooh: does there exist an orthogonal decomposition of the complex simple Lie algebras of type \(A_ n\), \(n\neq p^ m-1\), and \(C_ n\), \(n\neq 2^ m?\)
Reviewer: G.I.Zhitomirskij

17B20 Simple, semisimple, reductive (super)algebras
17B05 Structure theory for Lie algebras and superalgebras
20D08 Simple groups: sporadic groups