Integrable quantum spin chains, non-skew symmetric rr-matrices and quasigraded Lie algebras

Using general non-skew symmetric classical rr-matrices with a spectral parameter, we construct new quantum spin chains that generalize famous Gaudin spin chains. With the help of the special quasigraded Lie algebras, we construct new examples of the non-skew symmetric classical rr-matrices with a spectral parameter and explicit examples of new commuting Gaudin-type hamiltonians.