The conformal group of the ( p + q ) -dimensional space R p , q is S O ( p + 1 , q + 1 ) and its Lie algebra is s o ( p + 1 , q + 1 ) . The superconformal algebra is a Lie superalgebra containing the bosonic factor s o ( p + 1 , q + 1 ) and whose odd generators transform in spinor representations of s o ( p + 1 , q + 1 ) . Given Kac's classification of finite-dimensional simple Lie superalgebras, this can only happen for small values of p and q . A (possibly incomplete) list is