Integrable sigma models with Haantjes structure on $H_4$ Lie group

By solving algebraic relations for the conditions of Haantjes structure on a Lie algebra $\text{G}$ and by using the corresponding automorphism group we proceed to classify all inequivalent algebraic Haantjes structures on $\text{G}$. In this manner, we obtain 34 inequivalent algebraic Haantjes structures on the $h_4$ Lie algebra. We deform the chiral sigma model on a Lie group by using Haantjes structure on it. Then we try to obtain conditions on this structure such that the deformed sigma model remains to be integrable. Finally, using the $h_4$ Haantjes structures and solving this conditions three new integrable sigma models on the $H_4$ Lie group are obtained.