Abstract
Hussain, Yau, and Zuo introduced the Lie algebra L-k(V) from the derivation of the local algebra M-k(V) := O-n/(g+J(1)(g) + ... + J(k)(g)). To find the dimension of a newly defined algebra is an important task in order to study its properties. In this regard, we compute the dimension of Lie algebra L-5(V) and justify the sharp upper estimate conjecture for fewnomial isolated singularities. We also verify the inequality conjecture: delta(5)(V) < delta(4)(V) for a general class of singularities. Our findings are novel and an addition to the study of Lie algebra.