  Unconventional ferromagnetism and superconductivity in the imbalanced
kagome-lattice Hubbard model are investigated by the mean-field theory and
determinant quantum Monte Carlo method. Due to the asymmetric band structure of
kagome lattice, the spin-$z$ ferromagnetic order intrinsically exists in the
system, which is first enhanced by the interaction, and then continuously
destructed after reaching a maximum at a moderate interaction strength. In
contrast, the $xy$-plane ferromagnetism develops only above a critical
interaction, which is estimated to be $U_c/t=3.65 \pm 0.05$ by finite-size
scaling. We further verify the nature of the above transverse magnetic
transition, and demonstrate it belongs to the three-dimensional $XY$
universality class. Finally, we study the superconducting property, and reveal
the possible superconducting state has a triplet $f$-wave pairing symmetry. Our
results uncover the exotic quantum states induced by the interactions on kagome
lattice, and provide important insights regarding the interplay between
electronic correlations and geometry frustrations.
