Polynomial identities for quivers via incidence algebras

Key Points

• The aim is to demonstrate that the path algebra of a quiver shares polynomial identities with matrices.
• Analysis of path algebras in relation to matrix algebras.
• Investigation of polynomial identities of both algebra types.
• Comparison of properties between quivers and oriented cycles.
• Path algebras exhibit the same polynomial identities as algebra of matrices.
• Specifically, matrix algebras are polynomially identity equivalent to the path algebra of oriented cycles.