Naslov
Some structural results for nonsymmetric pairs of Lie algebras

Autori
Širola, Boris

Izvornik
Journal of algebra (0021-8693) 185 (1996); 571-582

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
semisimple Lie algebra ; Cartan pair ; absolutely simple ; Killing decomposition

Sažetak
We give some structural results on pairs (g, g1) consisting of a Lie algebra g and its subalgebra g1, reductive in g. For g1 absolutely simple we prove the (Killing-orthogonal) decomposition g=g1+p analogous to the orthogonal decomposition for symmetric Lie algebras. We characterize those pairs (g, g1), g1 semisimple which have the property that any Cartan subalgebra of g1 can uniquely be extended to a Cartan subalgebra of g. Using this the notion of a Cartan pair is introduced. We give the example of a Cartan pair consisting of a simple Lie algebra of type B3 and simple subalgebra of type G2. For that pair a number of structural results, similar as for semisimple symmetric Lie algebras, is given.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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