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Constructing semisimple subalgebras of real semisimple Lie algebras. (English) Zbl 1367.17008

Avitabile, Marina (ed.) et al., Lie algebras and related topics. Workshop on Lie algebras, in honor of Helmut Strade’s 70th birthday, Università degli Studi di Milano-Bicocca, Milano, Italy, May 22–24, 2013. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1023-0/pbk; 978-1-4704-2815-0/ebook). Contemporary Mathematics 652, 75-89 (2015).
Summary: We consider the problem of constructing semisimple subalgebras of real (semi-) simple Lie algebras. We develop computational methods that help to deal with this problem. Our methods boil down to solving a set of polynomial equations. In many cases the equations turn out to be sufficiently “pleasant” to be able to solve them. In particular this is the case for \(S\)-subalgebras.
For the entire collection see [Zbl 1330.17002].

MSC:

17B20 Simple, semisimple, reductive (super)algebras
17-08 Computational methods for problems pertaining to nonassociative rings and algebras
68W30 Symbolic computation and algebraic computation

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