Post-Lie algebra structures on solvable Lie algebra t(2,C)t(2,C)

The post-Lie algebra is an enriched structure of the Lie algebra introduced by Vallette. In this paper we give a complete classification of post-Lie algebra structures on solvable Lie algebra t(2,C)t(2,C), the Lie algebra of 2×22×2 upper triangular matrices. Furthermore, we discuss their isomorphism classes and obtain one necessary and sufficient condition.