  In this paper, we investigate the relationship between algebraic soliton
metrics and soliton metrics for geometric evolution equations on Lie groups.
After discussing the general relationship between algebraic soliton metrics and
soliton metrics, we investigate the cross curvature flow and the second order
renormalization group flow on simply connected three-dimensional unimodular Lie
groups, providing a complete classification of left invariant algebraic
solitons on such spaces.
