Calculation of Hamiltonian constraint and Mandelstam identities over extended knot families {psi(i)}(2)(2), {psi(i)}(3)(4) and {psi(i)}(4)(6)

The actions of the Hamiltonian constraint onto the members of the extended knot families {psi(i)}(2)(2), {psi(i)}(3)(4) and {psi(i)}(4)(6), and the check of their invariance under the Mandelstam identities are given in the extended loop representation of loop quantum gravity.