Given a row-finite higher-rank k-graph Λ, we define a commutative monoid TΛ which is a higher-rank analogue of the talented monoid of a directed graph. The talented monoid TΛ
Nearby in the stack
is canonically a
Zk
-monoid with respect to the action of state shift. This monoid coincides with the positive cone of the graded Grothendieck group
K0gr(KPk(Λ))
of the Kumjian-Pask algebra
KPk(Λ)
with coefficients in a field
k
. The aim of the paper is to investigate this
Zk
-monoid as a capable invariant for classification of Kumjian-Pask algebras. If
Zk
acts freely on
TΛ
(i.e., if
TΛ
has no nonzero periodic element), then we show that the
k
-graph
Λ
is aperiodic. The converse is also proved to be true provided
Λ
has no sources and
TΛ
is atomic. Moreover in this case, we provide a talented monoid characterization for strongly aperiodic
k
-graphs. We prove that for a row-finite
k
-graph
Λ
without sources, cofinality is equivalent to the simplicity of
TΛ
as a
Zk
-monoid. In view of this we provide a talented monoid criterion for the Kumjian-Pask algebra
KPR(Λ)
of
Λ
over a unital commutative ring
R
to be graded basic ideal simple. We also describe the minimal left ideals of
KPk(Λ)
in terms of the aperiodic atoms of
TΛ
and thus obtain a monoid theoretic characterization for
Soc(KPk(Λ)
) to be an essential ideal. These results help us to characterize semisimple Kumjian-Pask algebras through the lens of