Researches On Some Basic Properties Of Unitary Group

The main purpose of this thesis is to investigate properties of n-dimensionalunitary group. This thesis is arranged as follows:Chapter 1 provides some background information about problem-researching andstatement of our main results.In Chapter 2, we introduce some basic concepts and properties of unitarytransformation groups.In Chapter 3, some basic properties of unitary group (1, SU n;C) are obtained.In Chapter 4, firstly, we give the definition of convergence group SU(1,n;C) ,and then investigate its properties, especially discuss its maximal property. Severalproperties about elements in convergence groups acting in C~n are obtained, which aregeneration of properties about elements in convergence groups acting in R~n . By usingof these properties, we prove a kind of maximal property of subgroup in C~n .In Chapter 5, we study the discretness criterions for n-dimensional subgroup inPU(1,n;C) , these criterions are generated by the discreteness criterions forn-dimensional subgroup of Isom(H~n).