Integrable hamiltonian systems via quasi-graded Lie algebras on hyperelliptic curves

In the present work we construct new integrable systems using special quasi-graded algebras on hyperelliptic curves. In such a way we find new integrable hamiltonian systems, which are direct higher rank generalizations of the integrable systems of Steklov-Liapunov, associated with the e(3) algebra and Steklov-Veselov associated with the so(4) algebra. Besides we give hyperelliptic Lax representation for the generalized Euler tops, generalized Clebsh and  Neuman  systems.