In this work, using some tools of Lie theory, we compute the Lie algebra of the SHEARLET group regarding as a 3-fold
semidirect product Lie group. As we will see, it is a 3-fold semidirect sum of Lie algebras.
Keywords: SHEARLET group; Lie group; Lie algebra; Exponential map; Semidirect product
2020 MSC: Primary 42C40; Secondary 22E60