Central extensions of cotangent universal hierarchy: (2+12+1)-dimensional bi-Hamiltonian systems

We introduce the cotangent universal hierarchy that extends the universal hierarchy from [L. Martínez Alonso, A.B. Shabat, Phys. Lett. A 300 (1) (2002) 58, nlin.SI/0202008; A.B. Shabat, Theor. Math. Phys. 136 (2003) 1066; L. Martínez Alonso, A.B. Shabat, J. Nonlinear Math. Phys. 10 (2) (2003) 229, nlin.SI/0310036; L. Martínez Alonso, A.B. Shabat, Theor. Math. Phys. 140 (2) (2004) 1073, nlin.SI/0312043; A. Shabat, J. Nonlinear Math. Phys. 12 (Suppl. 1) (2005) 614]. Then we construct a (2+12+1)-dimensional double central extension of the cotangent universal hierarchy and show that this extension is bi-Hamiltonian. This yields, as a byproduct, the central extension of the original universal hierarchy.