osp ( 1 | 32 ) and Extensions of super - AdS 5 × S 5 algebra

The super-AdS5×S 5 and the four-dimensional N=4 superconformal algebras play important roles in superstring theories. It is often discussed the roles of the osp(1|32) algebra as a maximal extension of the superalgebras in flat background. In this paper we show that the su(2,2|4), the super-AdS5 × S 5 algebra or the superconformal algebra, is not a restriction of the osp(1|32) though the bosonic part of the former is a subgroup of the latter. There exist only two types of u(1) extension of the super-AdS5×S 5 algebra if the bosonic AdS5×S 5 covariance is imposed. Possible significance of the results is also discussed briefly. PACS: 11.25.-Hf;11.25.-Uv;11.25.-w;11.30.Pb;