Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Supervisors info:
Διονύσιος Λάππας Αναπλ. Καθηγητής (Επιβλέπων), Αντώνιος Μελάς Καθηγητής, Ιάκωβος Ανδρουλιδάκης Επίκουρος Καθηγητής
Original Title:
Θεωρήματα τύπου Palais – Kobayashi. Ομάδες Lie και Γεωμετρικές Δομές
Translated title:
Palais and Kobayashi theorems – Lie Groups and Geomertic Structures
Summary:
A Lie group is not a linear object, but it is determined “almost completely” by
a certain algebra, its Lie algebra. If a Lie group acts on a smooth manifold,
then a homomorphism of Lie algebras arises between the Lie algebra of Lie group
and the Lie algebra of all vector fields on the manifold. In special cases the
Lie algebra of Lie group can be considered a subalgebra of Lie algebra of the
manifold. Inversely, if we get a subalgebra g, which is finite dimensional, of
Lie algebra of a manifold, then reference is made to infinitesimal action. The
problem then is finding a Lie group which acts on manifold in a specific
manner. For this to be possible, necessary and sufficient conditions should be
applied: g must be finite dimensional and consist of complete vector fields.
The relevant studies are identified at theorems which have been formulated or
proved by R Palais and S. Kobayashi. Particulary, S. Kobayashi has identified a
large class of such cases as the parallelization.
Keywords:
Lie group, Lie algebra , Palais theorem , Kobayashi theorem , Fundamental vector fields
File:
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