Supervisors info:
Ιάκωβος Ανδρουλιδάκης (Επιβλέπων), Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Αντώνιος Μελάς Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Παναγιώτης Γιαννιώτης Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Summary:
A Lie algebra is the tangent space at the identity element of a manifold that admits a group structure in a way that the group operations of multiplication and inversion are smooth. We will present the constructive proof of Sophus Lie's Third Theorem as it is given in Duistermaat} and Kolk's book Lie Groups. It is the unique constructive proof of the third theorem that can be stated as; Every finite dimensional Lie algebra g is integrated to a simply connected lie group G.
To prove the theorem we will use the infinite dimensional Banach space of paths of the Lie algebra.
