Supersymmetry Algebra in Super Yang-Mills Theories

We compute supersymmetry algebra (superalgebra) in supersymmetric Yang-Mills theories (SYM) consisting of a vector multiplet including fermionic contribution in six dimensions. We show that the contribution of fermion is given by boundary terms. From six dimensional results we determine superalgebras of five and four dimensional SYM by dimensional reduction. In five dimensional superalgebra the Kaluza-Klein momentum and the instanton particle charge are not the same but algebraically indistinguishable. We also extend this calculation including a hyper multiplet and for maximally SYM. We derive extended supersymmetry algebras in these four dimensional SYM with the holomorphic coupling constant given in hep-th/9408099.