Bi-Hamiltonian structure of the N=2 supersymmetric α=1 KdV hierarchy

The N=2 supersymmetric α=1 KdV hierarchy in N=2 superspace is considered and its rich symmetry structure is uncovered. New nonpolynomial and nonlocal, bosonic and fermionic symmetries and Hamiltonians, bi-Hamiltonian structure as well as a recursion operator connecting all symmetries and Hamiltonian structures of the N=2 α=1 KdV hierarchy are constructed in explicit form. It is observed that the algebra of symmetries of the N=2 supersymmetric α=1 KdV hierarchy possesses two different subalgebras of N=2 supersymmetry.