Subelliptic sharp Gårding inequality on compact Lie groups

In this work we establish a subelliptic sharp G{a}rding inequality on compact Lie groups for pseudo-differential operators with symbols belonging to global subelliptic H\"ormander classes. In order for the inequality to hold we require the global matrix-valued symbol to satisfy the suitable classical nonnegativity condition in our setting. Our result extends to Sᵐρ,δ(G)-classes, 0≤ δ<ρ, the one in [26] about the validity of the sharp G{a}rding inequality for the class Sᵐ1,0(G). We remark that the result we prove here is already new and sharp in the case of the torus.