Standard Polynomials for Principal Subalgebras $\mathbb{K}Q_{\geq 1}$ of Path Algebras

We investigate standard polynomials for principal subalgebras of path algebras.

First, we use standard polynomials to study the $PI$-theory of principal subalgebras.

Then we describe the $St_2$-elements and $St_3$-elements of principal subalgebras, giving a characterization of their centers and 3-centers.

In addition, we apply these results to combinatorics on words of formal languages, obtaining some explanations from a combinatorial perspective.