In the new paper “Comment on “new integrable family in n-dimensional homogeneous Lotka-Volterra systems with Abelian Lie Algebra” [J. Phys. Soc. Jpn. 72 (2003) 973]” we present the new (generalized) Poisson structure and the Hamiltonian functions for the so-called generalized ladder system (GLS), obtaining also its first integrals as functionally independent Casimir functions for the associated Poisson algebra and thus proving the complete Liouville integrability of the GLS.

In this paper (arXiv:1202.2077) all real three dimensional Poisson-Lie groups are explicitly constructed and fully classified under group automorphisms by making use of their one-to-one correspondence with the complete classification of real three-dimensional Lie bialgebras given in [X. Gomez, J. Math. Phys. vol. 41, p. 4939 (2000)]. Many of these 3D Poisson-Lie groups are non-coboundary structures, whose Poisson brackets are given here for the first time. Casimir functions for all three-dimensional PL groups are given, and some features of several PL structures are commented.