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We continue the study of intersection algebras $\mathcal B = \mathcal B_R(I,J)$ of two ideals $I, J$ in a commutative Noetherian ring $R$. In particular,we exploit the semigroup ring and toric structures in order to calculatevarious invariants of the intersection algebra when $R$ is a polynomial ringover a field and $I,J$ are principal monomial ideals. Specifically, wecalculate the $F$-signature, divisor class group, and Hilbert-Samuel andHilbert-Kunz multiplicities, sometimes restricting to certain cases in order toobtain explicit formul{\ae}. This provides a new class of rings whereformul{\ae} for the $F$-signature and Hilbert-Kunz multiplicity, dependent onfamilies of parameters, are provided.

Computing The Invariants of Intersection Algebras of Principal Monomial Ideals