Extensions Of AT-Algebras And AT-Algebras

Recent years, a large number of classification results about non-simple C~*-algebras appeared. H. Lin and H. Su classified AT-algebras which often becomes an extensions of an A??-algebra by an AF-algebra. In this thesis, We show that there is an essential extension of an AT-algebra by an AF-algebra which is not an AT-algebra. We introduce a class of C~*-algebras which contains all AT-algebras. In general, they are infinite, neither AT-algebras nor simple purely infinite, however, a C~*-algebra in the class often becomes an extensions of an A??-algebra by an AF-algebra. We compute their invariants, and a classification is given to the class of C~*-algebras.