5 problems

Proper containment conjecture. The ideal of polynomial identities of the path algebra is properly contained in that of its principal subalgebra:

Let $R$ be the path algebra of an acyclic quiver, let $g$ be the onto map from admissible curves to indecomposable modules corresponding to positive real roots, and let $M$ be an i…

Let $R$ be the path algebra of a 2-complete quiver, and let $f$ be the bijection from indecomposable modules corresponding to positive real roots to admissible curves on the associ…

Let $\Lambda=KQ/I$ be a truncated path algebra with basic strong tilting module $T\in\Lambda\text{-}\operatorname{mod}$, and set … A full subcategory is contravariantly finite if e…

Let ${\mathbf{k}}{\mathbf{M}}$ be the path algebra of a semigroup ${\mathbf{M}}$, equipped with its topology. Consider the subcomplex of the Hochschild cochain complex consisting o…