The Automorphism Group Of The Lie Group T(D(V_N,F))

The purpose of this thesis is to determine maximal connected automorphism group of the Lie group T(D(Vn,F)) acting on the normal Siegel domains D(VN,F) simply and transitively. Denote t(D(VN, F)) the Lie algebra of T(D(VN, F)), by the theory of the Lie group, the maximal connected component of the automorphism group of the Lie group T(Z)(VN,F)) is isomorphic to the maximal connected automorphism group of the Lie algebra t(D(VN, F)), while the Lie algebra of Aut (t(D(VN, F))) is Der (t(D(VN,F))). It is enough to find the Lie algebra Der(t(D(VN, F))) for to determine the maximal connected automorphism group of the Lie group T(D(VN,F)). In this paper, suppose that the matrices in the normal matrix set of type N are all square matrices. Then we prove that the the maximal connected automorphism group of T(D(Vn, F)) is its maximal connected inner automorphism group.