Lie algebra of a family of one-parameter subgroups. (English) Zbl 0790.22005

Bureš, J. (ed.) et al., The proceedings of the 11th winter school on geometry and physics held in Srní, Czechoslovakia, January 5-12, 1991. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 30, 47-53 (1993).
It is known that the theory of Lie groups may be viewed essentially as a skill of deriving properties of a Lie group \(G\) from the structure of the family \(\Lambda(G)\) of all continuous one parameter subgroups of \(G\). The first etape of this procedure is introducing the appropriate real Lie algebra structure on \(\Lambda(G)\).
In the paper the authors present a new, mainly algebraic construction which associates to an arbitrary family \(\Lambda\) of continuous one parameter subgroups of a topological group \(G\) a real Lie algebra with gradation.
For the entire collection see [Zbl 0777.00026].
Reviewer: A.K.Guts (Omsk)


22E15 General properties and structure of real Lie groups
22A05 Structure of general topological groups
22E60 Lie algebras of Lie groups